Current Research in Gravito-Electromagnetic Space Propulsion
01.05.2014 19:18
Current Research in Gravito-Electromagnetic
Space Propulsion
Walter Dröscher and Jochem Hauser 1
Institut für Grenzgebiete der Wissenschaft, 6010 Innsbruck, Austria
Abbreviated Version 2
Figure 1. The figure shows a combination of two pictures. The first one shows an artist’s concept of two Jupiter like planets,
detected by NASA’s Spitzer Space Telescope. Spitzer captured for the first time, February 2007, enough light to take the spectra
of these two gas exoplanets, called HD 209458b and HD 189733b. These so-called "hot Jupiters" are like Jupiter, but orbit much
closer to their sun. Molecules were identified in their atmospheres. HD 189733b is about 63 light years away in the constellation
Vulpecula, and HD 209458b is approximately 153 light years away in the constellation Pegasus. The second picture, lower right,
depicts the principle of gravito-magnetic space propulsion. For further explanations see Fig. 5 of this paper.
1 Permanent address: Faculty Karl-Scharfenberg, Univ. of Applied Sciences, Salzgitter Campus, 38229 Salzgitter, Germany
2 Mathematical derivations were omitted in this abbreviated version
3 4 5
Abstract: Spaceflight, as we know it, is based on the century old rocket equation that is an embodiment of the conservation of
linear momentum. Moreover, special relativity puts an upper limit on the speed of any space-vehicle in the form of the velocity
of light in vacuum. Thus current physics puts severe limits on space propulsion technology.
This paper presents both recent theoretical and experimental results in the novel area of propulsion research termed gravitomagnetic
field propulsion comprising the generation of artificial gravitational fields. In the past, experiments related to any
kind of gravity shielding or gravito-magnetic interaction proved to be incorrect. However, in March 2006 the European Space
Agency (ESA) announced credible experimental results, reporting on the measurement of artificial gravitational fields (termed
gravito-magnetic fields), generated by a rotating Niobium superconductor ring that was subjected to angular acceleration. These
experiments were performed by M. Tajmar and colleagues from ARC Seibersdorf, Austria and C. de Matos from ESA, and
recently were repeated with increased accuracy.
Extended Heim Theory (EHT), published in a series of papers since 2002, predicted the existence of such an effect, resulting
from a proposed interaction between electromagnetism and gravitation. In EHT, which is a consequent extension of Einstein’s
idea of geometrization of all physical interactions, the concept of poly-metric developed by the German physicist B. Heim
is employed. As a consequence of this geometrization, EHT predicts the existence of six fundamental interactions. The two
additional interactions are identified as gravitophoton interaction, enabling the conversion of photons into a gravitational
like field, represented by two hypothetical gravitophoton (attractive and repulsive) particles, and the quintessence particle,
a weak repulsive gravitational like interaction (dark energy?). The experiments by Tajmar et al. (the artificial gravitational
force, however, was observed only in the circumferential direction of the superconducting ring) can be explained by the joint
generation of quintessence particles and gravitons. EHT is used to provide a physical model for the existence of the artificial
gravitational field, and to perform comparisons with experimental data.
In the next step, it is shown that the gravitophoton interaction could be used to devise a novel experiment in which the artificial
gravitational field would be directed along the axis of rotation, and thus this force could serve as the basis for a field propulsion
principle working without fuel. Based on this novel propulsion concept, missions to the international space station (LEO), the
planned moon basis, to Mars, and missions to the outer planets are analyzed. Estimates for the magnitude of magnetic fields
and necessary power are presented as well as for trip times.
PRESENT CONCEPTS OF SPACE PROPULSION
Current space transportation systems are based on the principle of momentum generation, regardless whether they
are chemical, electric, plasma-dynamic, nuclear (fission) or fusion, antimatter, photonic propulsion (relativistic)
and photon driven (solar) sails, or exotic Bussard fusion ramjets. The specific impulse achievable from thermal
systems ranges from some 500 s for advanced chemical propellants (excluding free radicals or metastable atoms),
approximately 1,000 s for a fission solid-core rocket (NERVA program [1] ) using hydrogen as propellant (for a
gas-core nuclear rocket specific impulse could be 3,000 s or higher but requiring very high pressures), and up to
200,000 s for a fusion rocket [2]. Although recently progress was reported in the design of nuclear reactors for plasma
propulsion systems [3] such a multimegawatt reactor has a mass of some 3106 kg and, despite high specific impulse,
has a low thrust to mass ratio, and thus is most likely not capable of lifting a vehicle from the surface of the earth.
For fusion propulsion, the gasdynamic mirror has been proposed as highly efficient fusion rocket engine. However,
recent experiments revealed magnetohydrodynamic instabilities [4] that make such a system questionable even from a
physics standpoint, since magnetohydrodynamic stability has been the key issue in fusion for decades. The momentum
principle combined with the usage of fuel, because of its inherent physical limitations, does not permit spaceflight to
be carried out as a matter of routine without substantial technical expenditure.
At relativistic speeds, Lorentz transformation replaces Galilei transformation where the rest mass of the propellant
is multiplied by the factor (1=
p
1¤v2=c2) that goes to infinity if the exhaust velocity v equals c, the speed of light in
vacuum. For instance, a flight to the nearest star at a velocity of some 16 km/s would take about 80,000 years. On the
other hand, a space vehicle with a mass of 106 kg at the high velocity of 105 km/s would take approximately 12.8 years
to reach this star. Its kinetic energy would amount to about 51021 J. Supplied with a 100 MW nuclear reactor, it
would take some 1.5 million years to generate this amount of energy. Current physics requires that energy conservation
is strictly adhered to and does not permit to extract energy from the vacuum. However the physical properties of the
3 Invited paper O-42, plenary session 7th International Symposium on Launcher Technologies 2007, 2-5 April 2007, Barcelona, Spain
4 ©Institut für Grenzgebiete der Wissenschaft Innsbruck, Austria 2007
5 The mathematical derivations in this paper rely on concepts explained in paper [11]. For lack of space these concepts are not presented here, see
www.hpcc-space.de for download.
vacuum are not known [18]. The energy density of the vacuum calculated by General Relativity (GR) and Quantum
Field Theory (QFT) differ by a factor of 10108, which means the error is in the exponent. Current physics clearly is open
to question. Moreover, it is obvious that if the speed of light cannot be transcended, interstellar travel is impossible.
We conclude with a phrase from the recent book on future propulsion by Czysz and Bruno [19]: If that remains the
case, we are trapped within the environs of our Solar System. In other words, the technology of spaceflight needs to be
based on novel physics that provides a novel propulsion principle. Most likely the physical properties of the vacuum
play an important role, although unknown at present.
Although advanced propulsion concepts as the ones described above must be pursued further, a research program
to look for fundamentally different propulsion principles is also both needed and justified, especially in the light of the
recent experiments by Tajmar et al. concerning the measurements of artificial gravitational fields [5], [6], [7], [8]. For
a popular description of this experimental work see [9], [10].
In addition, since 2002 ideas for a fundamental physical theory, termed Extended Heim Theory (EHT), predicting
two additional physical interactions that might give rise to the generation of artificial gravitational fields, have been
published, see for instance, [11], [12], [13], [14]. A popular description of this research may be found in [15], [16],
[17]. In the subsequent sections, EHT will be used to reproduce experimental values measured by Tajmar et al. and to
provide guidelines for a novel experiment that would serve as demonstrator for a propellantless propulsion device.
Needless to say, these ideas are highly speculative and their correctness can only be proved by experiment. However,
EHT makes precise predictions about the type and number of possible physical interactions. The proposed experiment
can be carried out with current technology to verify theoretical predictions.
PHYSICAL INTERACTIONS AND GEOMETRIZATION
In this section the fundamental structure of spacetime is discussed. The main idea of EHT is that spacetime possesses
an additional internal structure, described by an internal symmetry space, dubbed Heim space, denoted H8, which
is attached to each point of the spacetime manifold. The internal coordinates of H8 depend on the local (curvilinear)
coordinates of spacetime. This is analogous to gauge theory in that a local or gauge transformation is used. In gauge
theory it is the particles themselves that are given additional degrees of freedom, expressed by an internal space.
Consequently in the geometrization of physics, it is spacetime instead of elementary particles that has to be provided
with internal degrees of freedom. The introduction of an internal space has major physical consequences. The structure
of H8 determines the number and type of physical interactions and subsequently leads to a poly-metric. This means that
spacetime comprises both an external and internal structure. In general, only the external structure is observed,
but as has long been known experimentally, matter can be generated out of the vacuum. This is a clear sign that
spacetime has additional and surprising physical properties. Therefore, any physical theory that aims at describing
physical reality, needs to account for this fact. Since GR uses pure spacetime only, as a consequence, only part of the
physical world is visible in the form of gravitation.
This idea was first conceived by the German physicist B. Heim. A similar principle was mentioned by the Italian
mathematician B. Finzi. The poly-metric tensor resulting from this concept is subdivided into a set of sub-tensors, and
each element of this set is equivalent to a physical interaction or particle, and thus the complete geometrization of
physics is achieved. This is, in a nutshell, the strategy chosen to accomplish Einstein’s lifelong goal of geometrization
of physics 6. It must be noted that this approach is in stark contrast to elementary particle physics, in which particles
possess an existence of their own and spacetime is just a background staffage [32]. In EHT, considered as the
natural extension of GR, matter simply is a consequence of the hidden physical features of spacetime. These two
physical pictures are mutually exclusive, and experiment will show which view ultimately reflects physical reality. It
is, however, well understood that the concept of a pointlike elementary particle is highly useful as a working hypothesis
in particle physics.
6 There is of course a second aspect, namely the quantization of the spacetime field.
Geometrization of Space, Time, and Energy
In GR the geometrical structure of spacetime leads to a single metric that describes gravitational interaction.
Einstein’s pioneering efforts in the geometrization of physics revealed themselves unsuccessful [22] when more
interactions were discovered, and attempts to geometrize physics were abandoned. Einstein did not succeed in
constructing a metric tensor that encompassed all physical interactions. At almost the same time, B. Heim at the
space congress in Stuttgart, Germany 1952 and in [23], and also B. Finzi, 1955, see the recent book [24], published
similar ideas on the construction of a generalized metric tensor. Heim published further details of his theory in [25],
[26] constructing a poly-metric tensor in a 6D space. In collaboration with Heim this idea was extended to 8D by the
first author.
Einsteinian spacetime [20], [21] is indefinitely divisible and can be described by a differentiable manifold. In the
following derivation, which relates the metric tensor to physical interactions, this classical picture is used, though
most likely spacetime is a quantized field. The quantization of spacetime seems to play a role in the concept of
hyperspace or parallel space [14], which might allow superluminal velocities, but is not treated in this paper. GR can
be summarized by the single sentence: matter curves spacetime.
In curved spacetime the metric is written in the form
ds2 = gmndhmdhn (1)
where gmn is the metric tensor, h1;h2;h3 are the spatial coordinates, and h4 is the time coordinate. These coordinates
can be curvilinear. Einstein summation convention is used, i.e., indices occurring twice are summed over. From the
strong equivalence principle it is known (for instance see [27]) that at any point in spacetime a local reference frame
can be found for which the metric tensor can be made diagonal, i.e., gmn = hmn where hmn is the Minkowski tensor, 7
and reference coordinates are locally Cartesian (x1; x2; x3; x4) = (x; y; z; ct). This is equivalent to a transformation
between the two sets of coordinates, namely
dxm = Lm
n dhn and Lm
n =
¶ xm
¶hn (2)
In the free fall frame of the x coordinates the acceleration is 0, and thus the equation of motion simply is
d2xm
dt2 = 0 and ds2 = hmn dxmdxn (3)
where t denotes proper time, i.e., the time registered by a clock in its own reference frame. This means the clock is
stationary in this frame, and the time measured is the time shown on the clock’s dial. In order to obtain the equation of
motion for curvilinear coordinates h, one only needs to insert the transformation relations, Eq. (2), into Eq. (3), which
results in the geodesic equation
d2ha
dt2 +Gamn
dhm
dt
dhn
dt
= 0 (4)
where the Gam
n are the well known Christoffel symbols or affine connections. Rewriting the geodesic equation (4) in
the form
d2ha
dt2 = f a with f a = ¤Gam
n
dhm
dt
dhn
dt (5)
and comparing Eq. (5) with the equation of motion for a free falling particle Eq. (3), the right hand side of Eq. (5)
can be regarded as a force coming from a physical interaction, which has caused a curvature of the surrounding space,
marked by the presence of nonzero Christoffel symbols. The left hand side of equation (5) can be written as mIa where
mI denotes inertial mass and a is acceleration. Multiplying f a by its proper charge results in the equation of motion
for the respective physical interaction. In the case of gravity, because of the equality of inertial and gravitational mass,
charges on the left and right hand sides cancel out. For all other physical interactions this is not the case. In that respect
7 Minkowski tensor hmn must not be confused with curvilinear coordinates hm
gravity has a unique role, namely that it curves also the surrounding space. For all other physical interactions, if
pointlike charges are assumed (classical picture), space is curved only at the location of the charge.
One major point of course is that the relation x = x(h) as used in GR delivers only a single metric, which
Einstein associated with gravitation. The fundamental question is, therefore, how to construct a metric tensor that
gives rise to all physical interactions. The answer lies in the fact that in EHT there exists an internal space H8.
Therefore, in EHT the relation between coordinates x and h is x = x(x (h)). In contrast to GR, EHT employs a
double transformation as specified in Eq. (7). From this double transformation a set of different metric tensors can
be constructed, which, in turn, lead to a set of individual geodesic equations having the same structure as Eq. (5), but
depending on the specific charge and Christoffel symbols inherent to this specific physical interaction. An individual
equation of motion will have the form
mI
d2hm
dt2 = ec f m
c with m = 1; :::;4 (6)
where ec denotes the specific charge of the interaction and quantities f m
c are the associated Christoffel symbols 8
i.e., they stand for the curvature of space generated by this interaction. The total number of physical charges ec is
determined by the subspace structure of H8 in concert with combination rules to constructing a metric that has physical
meaning. Eq. (6) describes a very difficult physical problem. First, the number of physical charges and their coupling
constants need to be determined. Without further demonstration, only a few facts are stated. There exist, according
to EHT, eight charges, namely three color charges for the quarks, two weak charges, one electric charge, and two
charges for gravitation, where one naturally is the gravitational charge. The second charge could be inertia or the
charge of the vacuum. This is not clear at present. The double transformation as given in Eq. (7) represents the particle
aspect and leads to eigenvalue equations whose eigenvalues have dimension of inverse length. In these eigenvalue
equations, the Christoffel symbols occur. Using the inverse of the Planck length expressed as mpc=¯h, results in a
correspondence between inverse length and mass. Since particles and fields form a unity, the transformation from
spacetime into internal space, M !H8, should represent the field aspect, because derivatives of internal coordinates
x a;a = 1; :::;8 with respect to curvilinear coordinates h lead to an expression
ea
c
mI
ha
ik. The ha
ik denote deviation from
the flat metric, and physically represent the tensor potential of the charge ea
c with mI as associated inertial mass.
The metric coefficients thus assume energy character. This short discussion implies a comprehensive mathematical
program, namely the determination and solution of the above mentioned eigenvalue equations as well as the derivation
of the tensor potentials for the interactions. The task is not yet finished, but this brief discussion should have conveyed
an idea how the introduction of an internal symmetry space leads to a correspondence between geometry and physical
quantities. 9 10
This approach is substantially different from GR and leads to the complete geometrization of physical
interactions.
Naturally, the number and type of interactions depend on the structure of internal space H8 whose subspace
composition is determined in the subsequent section. Contrary to the ideas employed in String theory, see for example
[28], H8 is an internal space of 8 dimensions that, however, governs all physical events in our spacetime.
The crucial point lies in the construction of the internal space whose subspace composition should come from basic
physical assumptions, which must be generally acceptable. In other words, GR does not possess any internal structure,
and thus has a very limited geometrical structure, namely that of pure spacetime only. Because of this limitation, GR
cannot describe other physical interactions than gravity, and consequently needs to be extended. EHT in its present
form without any quantization, i.e., not using a discrete spacetime, reduces to GR when this internal space is omitted.
The metric tensor, as used in GR, has purely geometrical means that is, it is of immaterial character only, and does
not represent any physics. Consequently, the Einsteinian Geometrization Principle (EGP) is equating the Einstein
curvature tensor, constructed from the metric tensor, with the stress tensor, representing energy distribution. In this
way, the metric tensor field has become a physical object whose behavior is governed by an action principle, like that
8 The equation of motion describes a particle of mass mI with charge ec, subjected to the respective field of this interaction, represented by its
proper Christoffel symbols.
9 The mathematical framework to determine the charges and to obtain the correspondence between geometry and physics is quite involved. In
general internal coordinates are described by quaternions.
10 There is an interesting question, namely: What is the Hermetry form of the vacuum field ? If the vacuum has an energy density different from
zero, it should not be the case that its Christoffel symbols are 0. However, we feel, in order to answer this question, a quantization procedure for Eq.
(6) has to be established.
of other physical entities. In EHT the internal space H8 is associated with physics through the introduction of three
fundamental length scales, constructed from Planck quantities.
FUNDAMENTAL INTERACTIONS AND HERMETRY FORMS
The introduction of basic physical units is in contradiction to classical physics that allows infinite divisibility. As a
consequence, measurements in classical physics are impossible, since units cannot be defined. Consequently, Nature
could not provide any elemental building blocks to construct higher organized structures, which is inconsistent with
observation. Thus the quantization principle is fundamental for the existence of physical objects.
Next, we introduce four basic principles, from which the nature of H8 can be discovered. In contrast to GR, EHT is
based on the following four simple and general principles, termed the GODQ principle 11 of Nature. These principles
cannot be proved mathematically, but their formulation is based on generally accepted observations and intend to
reflect the workings of Nature.
i. Geometrization principle for all physical interactions,
ii. Optimization (Nature employs an extremum principle),
iii. Dualization (duality, symmetry) principle (Nature dualizes or is asymmetric, bits),
iv. Quantization principle (Nature uses integers only, discrete quantities).
From the duality principle, the existence of additional internal symmetries in Nature is deduced, and thus a higher
dimensional internal symmetry space should exist, whose exact structure will now be determined. In GR there exists a
four dimensional spacetime, comprising three spatial coordinates with positive signature (+) and the time coordinate
with negative signature (-). It should be remembered that the Lorentzian metric of R4 has three spatial (+ signature)
and one time-like coordinate (- signature) 12. The corresponding metric is called Minkowski metric and the spacetime
associated with this metric is the Minkowski space. The plus and minus signs refer to the (local) Minkowski metric
(diagonal metric tensor, see Eq. (1). Therefore, the squared proper time interval is taken to be positive if the separation
of two events is less than their spatial distance divided by c2. A general coordinate system for a spacetime manifold,
M, needs to be described by curvilinear coordinates hm with m = 1; ::;4 and h = (hm ) 2 M.
The set of 8 internal coordinates for H8 is determined by utilizing the GODQ principle. There are three internal
spatial coordinates, x 1;x 2;x 3, and the internal time coordinate x 4. The other four coordinates are introduced to
describing the degree of organization and information exchange as observed in Nature.
In summary, internal coordinates x i with i=1; :::;4 denote spatial and temporal coordinates, x i with i=5;6 denote
entelechial and aeonic coordinates, and x i with i = 7;8 denote the two information coordinates in H8, mandating
four different types of coordinates. With the introduction of a set of four different types of coordinates, the space
of fundamental symmetries of internal space H8 is fixed. In the next section, the set of metric subtensors of H8 is
constructed, each of them describing a physical interaction or particle. Thus the connection between physical space
and physics (symmetries) is established in a way foreseen by Einstein. Physical space is responsible for all physical
interactions. However, in order to reach this objective, spacetime had to be complemented by an internal space H8 to
model its physical properties. Once the internal space with its set of coordinates has been determined, everything else
is fixed, because Eq. (7) is a direct consequence of H8 .
It should be noted that a dimensional law can be derived that does not permit the construction of, for instance,
a space H7 [26]. In order to determine the number of admissible Hermetry forms and their physical meaning, we
proceed as follows. As was shown above, Heim space, H8, comprises four subspaces, denoted as R3 with coordinates
x 1;x 2;x 3, T1 with coordinate x 4, S2 with coordinates x 5;x 6 , and I2 with coordinates x 7;x 8: In order to construct a
physically meaningful metric sub-tensor (also called Hermetry form), it is postulated that coordinates of internal
spaces S2 or I2 must be present in any metric subtensor to generate a Hermetry form. From this kind of selection rule,
it is straightforward to show that 12 Hermetry forms can be generated, having direct physical meaning. In addition,
there are three degenerated Hermetry forms that describe partial forms of the photon and the quintessence potential,
11 briefly stated: God quantizes.
12 Signatures are not unique. Coordinate signatures may be reversed. Numbering of coordinates was chosen such that coordinates of positive
signature are numbered first.
for details see Tables 2, 4 of ref. [11]13. Hermetry form 16 is reserved for the Higgs particle that should exist, whose
mass was calculated at 182:70:7 GeV. For instance, the Hermetry form (photon metric) comprises only coordinates
from subspaces T1 , S2 , and I2 and is denoted by H7(T1 S2 I2). The neutral gravitophoton Hermetry form is
given by H5(S2 I2). Since gravitophoton and photon Hermetry forms are described by different coordinates, they
lead to different Christoffel symbols, and thus to different geodesic equations, see Eq. (6). Furthermore, if there were
a physical process to eliminate the T1 coordinates, i.e., the corresponding Christoffel symbols are 0, the photon would
be converted into a gravitophoton. This is how mixing of particles is accomplished in EHT. We believe this to be
the case in the experiments by Tajmar et al. The fundamental question, naturally, is how to calculate the probability
of such a process, and to determine the experimental conditions under which it can take place. Hermetry forms alone
only provide the potential for conversion into other Hermetry forms, but nothing is said about physical realization.
In any case, if Hermetry forms describe physical interactions and elementary particles, a completely novel scenario
unfolds by regarding the relationships between corresponding Hermetry forms. Completely new technologies could be
developed converting Hermetry forms. In the section about the proposed gravito-magnetic field propulsion experiment,
an experiment utilizing a rotating disk is described to convert photons into positive (repulsive) and negative (attractive)
gravitophotons that should generate an artificial gravitational field along the axis of rotation.
Fig. (2) depicts the six fundamental forces predicted by EHT. From the neutral gravitophoton metric and from the
forces measured in the experiments, it is deduced that the gravitophoton decays into a graviton (H1) and a quintessence
(H9, repulsive) particle. Fig. (3) shows the set of metric-subspaces that can be constructed. The word Hermetry is a
combination of hermeneutics and geometry that is, a Hermetry form stands for the physical meaning of geometry.
Each Hermetry form has a direct physical meaning, for details see refs. [11], [13], [14].
Double Coordinate Transformation
In this section the mathematical details of constructing Hermetry forms are presented. The concept of an internal 8D
space, comprising four subspaces, leads to a modification of the general transformation being used in GR. In GR there
are two sets of coordinates, Cartesian coordinates x and curvilinear coordinates h linked by a relation between their
corresponding coordinate differentials, Eqs. (1, 2). If Heim space were not existing, the poly-metric of EHT collapsed
to the mono-metric of GR.
The existence of internal space H8 demands a more general coordinate transformation from a spacetime manifold
14 M to a manifold N via the mapping M (locally R4 ) ! H8 ! N (locally R4 ). In EHT, therefore, a double
transformation, Eq.(7), involving Heim space H8 occurs. The associated global metric tensor, Eq. (7), does not have
any physical meaning by itself. Instead, by deleting corresponding terms in the global metric, the proper Hermetry
form is eventually obtained. The global metric tensor is of the form
gik =
¶ xm
¶ x a
¶ x a
¶hi
¶ xm
¶ x b
¶ x b
¶hk (7)
where indices a;b = 1; :::;8 and i;m;k = 1; :::;4 and gik comprises 64 components. The tensor with all 64 terms
does not have a physical meaning.
A single component of the metric tensor belonging to one of the four subspaces is given by Eq. (8). Only special
combinations of the gab
ik reflect physical quantities. Because of the double transformation, each physically meaningful
metric does comprise a different subset of the 64 components. In other words, depending on the Hermetry form, a
specified number of components of the complete metric tensor in spacetime, Eq. ((7), are set to zero. Hence, each
Hermetry form is marked by the fact that only a subset of the 64 components is present. Therefore each Hermetry
form leads to a different metric in the spacetime manifold and thus describes different physics. This is why Eq. ((7)
is termed the poly-metric tensor. It serves as a repository for Hermetry forms. This construction principle is totally
different from Einstein’s approach, and only in the special case of vanishing space H8 , EHT reduces to GR.
gab
ik =
¶ xm
¶ x (a)
¶ x (a)
¶hi
¶ xm
¶ x (b)
¶ x (b)
¶hk (8)
13 Tables 1-4 of ref. [11] were omitted from this paper because of lack of space
14 in the concrete case of GR spacetime manifold M4 would be used
Figure 2. EHT predicts, as one of its most important consequences, two additional, gravitational like interactions and the existence
of two messenger particles, termed gravitophoton and quintessence. That is, there is a total of six fundamental physical interactions.
The name gravitophoton has been chosen because of the type of interaction, namely the transformation of the electromagnetic field
(photon) into the gravitational field (gravitophoton). The arrow between the gravitophoton and electromagnetic boxes indicates
the interaction between these messenger particles that is, photons can be transformed into gravitophotons. In the same way
the quintessence interaction can be generated from gravitons and positive gravitophotons (repulsive force). It is assumed that
first a neutral gravitophoton is generated that decays into a pair of negative (same sign as gravitational potential) and positive
gravitophotons.
The poly-metric tensor can be written as
gik =
8å
a;b=1
ga;b
ik (9)
A single Hermetry form is given by
gik(Hl) :=
8å
a;b2Hl
gab
ik (10)
It should be mentioned that each Hermetry form itself comprises a set of submetric tensors that are intrinsic to this
Hermetry form. In how far this is an indication for further substructures is not known at the moment. In any case, there
are three additional Hermetry forms that we denoted as degenerate Hermetry form. They are describing neutrinos
and two novel fields that were identified as conversion (probability) amplitudes wph_gp and wgp_q. The first amplitude
stands for the probability of converting photons into gravitophotons, the second one denotes the probability for a
gravitophoton to decay into a graviton and quintessence particle. These conversion equations play a major role in the
explanation of the experiments by Tajmar et al. as well as in the proposed field propulsion experiment.
Physical Meaning of Hermetry Forms
Here, we only can give a brief discussion of the meaning of Hermetry forms. Each of the 15 admissible combinations
(not counting the Higgs particle) of metric subtensors (Hermetry forms) is ascribed a physical meaning, see Tables 1-4
in ref. ([11]). A Hermetry form is denoted by Hl with l =1; :::;15 is used. Indices 1-12 are obtained from the definition
of the Hermetry forms, see Fig. (3). Each Hermetry form Hl is interpreted as physical interaction or particle, extending
the interpretation of metric employed in GR to the poly-metric, coming from the combination of external physical
spacetime and internal space that is, the interaction of space H8 with four-dimensional spacetime M4. Internal space
H8 is a factored space that is, it is represented as H8 = R3 T1 S2 I2. This factorization of H8 into one space-like
manifold R3 and three time-like manifolds T1, S2 and I2 is inherent to the structure of H8. Each subspace can be
associated with a symmetry group. H8 would be associated with group O(8), which in turn is also factored. For the
construction of the individual Hermetry forms, a selection rule is used, namely any physically meaningful Hermetry
form must contain space coordinates from S2 or I2. This means, for a physical process to become manifest in
spacetime, a pair of the transcoordinates (entelechial, aeonic or information coordinates) must occur in its metric, i.e.,
in its Hermetry form. Each individual Hermetry form is equivalent to a physical potential or a messenger particle. It
should be noted that a Hermetry form in space S2 I2 describes gravitophotons, and a Hermetry form constructed
from space S2 I2 T1 represents photons, see Table 2 in ref. ([11]). This is an indication that, at least on theoretical
arguments, photons can be converted into gravitophotons, if the time dependent part T1 of the photon metric can be
canceled. Fig. (3) shows the possible Hermetry forms in EHT.
Conversion Equations for Hermetry Forms
In the section above, the physical meaning of Hermetry forms was discussed. Regarding the Hermetry forms for the
photon, H7, and the gravitophoton, H5, see Table 2 in [11], it is straightforward to see that if all metric subcomponents
containing the time coordinate in the metric tensor of the photon are deleted, the metric of a neutral 15gravitophoton
is generated. The fundamental question is, of course, how this mathematical process can be realized as a physical
phenomenon.
Regarding further the Hermetry form of the neutral gravitophoton, it should be possible that under certain circumstances
this neutral gravitophoton becomes unstable and decays. According to its metric form, a neutral gravitophoton
can decay through two channels. In one case, a graviton and a quintessence particle can be generated. In the second
case, a positive (repulsive) and a negative (attractive) gravitophoton can be produced. The former seems to occur in
Tajmar’s experiments, see section below, and the latter case should happen in the proposed field propulsion experiment
outlined, see corresponding section.
A conversion of photons into gravitophotons should be possible in two ways, namely via Fermion coupling
according to Eqs. (12), (13) and through Boson coupling, described by Eqs. (14), (15). These equations are termed
conversion equations. The three conversion amplitudes have the following meaning: The first equation, Eq. (12) is
obtained from EHT in combination with considerations from number theory, and predicts the conversion of photons
into gravitophoton particles, published already in 1996 [35] while the second equation, Eq. (13), is taken from Landau
[36] where the probability amplitude wgp for the photon coupling is given by the well known relation
w2
ph =
1
4pe0
e2
¯hc
: (11)
The physical meaning of Eqs. (12), (13) lies in the production of N2 gravitophoton particles through the polarization
of the vacuum. This conversion process is termed Fermion coupling, because it is assumed that the production
of gravitophotons takes place at the location of a virtual electron. This process is described in detail in references [11],
[13], and [12]. As was further discussed in these references, the magnitude of the necessary magnetic induction, m0H,
15 a gravitophoton is termed neutral if it does not interact with matter
Figure 3. In EHT, each point in spacetime is associated with an internal Heim space H8 that has eight internal coordinates. These
coordinates are interpreted as energy coordinates. The Planck length lp is associated with spatial coordinates of space R3 , the
Planck length lt with the time coordinate of space T1 , and Planck length lmp with the four additional organization and information
coordinates (negative) signature, which give rise to two additional subspaces denoted as S2 and I2, respectively. Hence, Heim space
H8 comprises four subspaces, namely R3 , T1 , S2 , and I2. The 8 coordinates x n of H8 themselves are functions of the curvilinear
coordinates hm that is, x n = x n(hm) of physical spacetime, manifold M4. The picture shows the complete set of metric-subspaces
that can be constructed from the poly-metric tensor, Eq. (7). Each submetric is denoted as Hermetry form, which has a direct
physical meaning, see Table 2 in [11]. In order to construct a Hermetry form, either internal space S2 or I2 coordinates must be
present. In addition, there are three degenerated Hermetry forms, see Table 4 in [11] that are only partial metric forms of the photon
and the quintessence potential. They allow the conversion of photons into gravitophotons as well as the decay of gravitophotons
into gravitons and quintessence particles.
in order to obtain sufficient gravitophoton production to generate a sizeable gravitophoton force (or Heim-Lorentz
force), is in the range of 20 to 50 T, and thus is most likely beyond current technology.
wph(r)¤wph_gp = Nwgp (12)
wph(r)¤wph_gp = Awph (13)
Eq. (13) and the function A(r) can be obtained using Landau’s [36] radiation correction with numerical values for
A ranging from 10¤3to 10¤4. Eqs. (12) and (13) can be interpreted such that an electromagnetic potential (photon)
containing probability amplitude Awph can be converted into a neutral gravitophoton with associated probability
amplitude Nwgp. Landau’s equation, Eq. (13), is responsible for the additional charge, coming from the reduced
shielding of the vacuum.
When we analyzed the experiments by Tajmar et al. it became clear that there seems to be a second way to generate
a gravitophoton force, namely using Cooper pairs to trigger the production of neutral gravitophotons. Because of
the coupling through Cooper pairs, this conversion is dubbed Boson coupling, and is specified by Eqs.(14) and (15). It
turned out that the conversion of photons into gravitophotons through Boson coupling has substantially lower technical
requirements. Instead of changing the conversion amplitude wph(r) by reducing the distance between virtual electron
and proton below the Compton wavelength, lC, (for mathematical details see the above mentioned references), it is
now the value of the probability amplitude wph_gp that changes. In general, i.e., without the presence of Cooper pairs,
wph_gp = wph and, according to Eq. (15), the probability for gravitophoton production is 0. For the production process
to take place, it is assumed that the onset of superconducting - with its formation of Cooper pairs - has an effect
similar to the creation of electron-positron pairs responsible for an increased coupling, and therefore an increase in the
magnitude of the coupling constant or charge. This is in analogy to vacuum polarization where the magnetic field is
strong enough to produce virtual electron-positron pairs, creating an excess charge. It should be noted that coupling
values k and a were derived some ten years ago, and were published by Heim and Dröscher 1996 in [35], see Eq. (11)
p. 64, Eq. (15) p. 74, and Eq. (16) p. 77.
wph¤wph_gp = iNwgp (14)
wph¤wph_gp = i
1
(1¤k)(1¤ka) ¤1
wph (15)
where i denotes the imaginary unit. Eqs. (13) and (15) reflect the basic difference between Fermion and Boson
coupling. In Fermion coupling the additional charge is produced by the vacuum of spacetime, while in Boson coupling
the additional charge comes from an increase of charge of the Cooper pairs through the Higgs mechanism. The Boson
coupling therefore is a condensed matter phenomenon. This means that for Boson coupling the probability amplitude
(charge) wph remains unchanged, which is in contrast to Fermion coupling. Instead, as can be seen from Eq. (15), it
is the probability amplitude wph_gp that is modified when the superconducting state is reached. Through the Higgs
mechanism, as was first stated by P.W. Anderson (1958) and later by Higgs, the photon assumes mass 16 and thus
via Eq. (11) the electromagnetic coupling gets stronger, and, in turn, the electric charge e becomes larger. Therefore,
Cooper pairs are subjected to an increase in charge.
EHT AND GRAVITO-MAGNETIC EXPERIMENTS
In a recent experiment (March 2006), funded by the European Space Agency and the Air Force Office of Scientific
Research, Tajmar et al. [7] report on the generation of a toroidal (tangential, azimuthal) gravitational field in a rotating
accelerated (time dependent angular velocity) superconducting Niobium ring. In July 2006, in a presentation
at Berkeley university, Tajmar showed improved experimental results that confirmed previous experimental findings.
Very recently, October 2006 [6] and February 2007 [5] the same authors reported repeating their experiments employing
both accelerometers as well as laser ring-gyros that very accurately measured the gravito-magnetic field. The
acceleration field was clearly observed, and its rotational nature was determined by a set of four accelerometers in the
plane of the ring.
Since the experiment generates an artificial gravitational field, which is in the plane of the rotating ring, see below,
it cannot be used as propulsion principle. It is, however, of great importance, since it shows for the first time that a
gravitational field can be generated other than by the accumulation of mass.
In this section we will present a theoretical derivation based on EHT to both qualitatively and quantitatively explain
the experiments. In addition, a comparison with the measured data will be presented. The experimental outcome was
explained by Tajmar and de Matos, postulating that the Higgs mechanism were responsible for the graviton to gaining
mass. This effect, [7], was termed the gyro-magnetic London effect. According to these authors, this phenomenon is
the physical cause for the existence of the measured gravitational field. We will discuss these arguments and compare
with the explanation given by EHT, which assumes the artificial gravitational field to be caused by the two gravitational
additional interactions predicted by EHT.
In the following, a derivation from first principles is presented, using the concept of neutral garvitophoton and its
subsequent decay into graviton and quintessence particles, which can be seen directly from the Hermetry form of the
neutral gravitophoton and the direction of the artificial gravitational field. However, for this experiment a coupling
to bosons (Cooper pairs) occurs. Deriving this effect from gravitophoton interaction, a physical interpretation can be
given that explains both qualitatively and quantitatively the experimental results. Moreover, theoretical considerations
obtained from EHT lead to the conclusion that an experiment should be possible to generate a gravitational field
acting parallel to the axis of rotation of the rotating ring, see Fig. 5, and thus, if confirmed, could serve as a
demonstrator for a field propulsion principle.
In this field propulsion experiment the superconducting rotating ring of the experiments by Tajmar et al. is replaced
by an insulating disk of a special material in combination with a special set of superconducting coils. According to
16 There is an alternative explanation. In a very recent article by Kane [38] the existence of electrically charged Higgs bosons is assumed. Due to
the Higgs mechanism there might be an interaction of these bosons with Cooper pairs, increasing their electric charge.
Figure 4. Rotating superconducting torus (Niobium) modified from Tajmar et al., see ref. [5]. All dimensions are in mm. A
cylindrical coordinate system (r;Q; z) with origin at the center of the ring is used. In-Ring accelerometers measured a gravitational
acceleration of ¤1:410¤5g in the azimuthal (tangential, Q) direction when the ring was subjected to angular acceleration, see
Fig. 8(a) ref. [5] for the so called curl configuration that comprises a set of four accelerometers. In an earlier publication, see Fig.
4a) in [7], an acceleration field of about ¤1010¤5g was measured for a single accelerometer. According to M. Tajmar, the curl
value should be used. The acceleration field did not depend on angular velocity w. No acceleration was measured in the z-direction
(upward). The more recent experiment employed a set of 4 in-Ring accelerometers and confirmed the rotational character of this
field. When the direction of rotation was reversed, the acceleration field changed sign, too.
EHT, the physical mechanism is different in that the neutral gravitophoton now decays into a positive (repulsive) and
negative (attractive) gravitophoton, which causes the artificial gravitational field to point in the axis of rotation. EHT is
used to calculate the magnitude and direction of the acceleration force and provides guidelines for the construction of
the propulsion device. The coupling to bosons is the prevailing mechanism. Experimental requirements, i.e., magnetic
induction field strength, current densities, and number of turns of the solenoid, are substantially lower than for fermion
coupling (here the vacuum polarization is employed to change the coupling strength via production of virtual pairs
of electrons and positrons) that was so far assumed in all our papers, see, for instance, refs. [12], [13], [14]. Fig.
4 depicts the experiment of Tajmar et al., where a superconducting ring is subject to angular acceleration and an
artificial gravitational field was measured in the plane of the ring in circumferential direction, counteracting the
angular acceleration, i.e., following some kind of gravitational Lenz rule. Fig. 5 describes the experimental setup for
the field propulsion device where an insulating disk rotates directly above the superconducting solenoid. In both cases
an artificial gravitational field arises, generated by gravitophoton interaction. The major difference between the two
experiments is that Tajmar et al. need to accelerate the rotating superconducting ring producing the gravitational field
in azimuthal direction, while the field propulsion experiment uses a uniformly rotating disk, generating an artificial
gravitational field in the axis of rotation. It is the latter experiment that could serve as the basis for a novel propulsion
technology - if EHT is correct.
The Gravito-Magnetic Experiment
In the experiments by Tajmar et al. it is shown that the acceleration field vanishes if the Cooper pairs are destroyed.
This happens when the magnetic induction exceeds the critical value BC(T), which is the maximal magnetic induction
that can be sustained at temperature T, and therefore dependents on the material. For temperatures larger than the
critical temperature TC superconductivity is destroyed, too. The rotating ring no longer remains a superconductor and
the artificial gravitational field disappears.
Considering the Einstein-Maxwell formulation of linearized gravity, a remarkable similarity to the mathematical
form of the electromagnetic Maxwell equations can be found. In analogy to electromagnetism there exist a gravitational
scalar and vector potential, denoted by Fg and Ag, respectively [34]. Introducing the corresponding gravitoelectric and
gravitomagnetic fields
e := ¤ÑFg and b := ÑAg (16)
the linearized version of Einstein’s equations of GR can be cast in mathematical form similar to the Maxwell equations
of electrodynamics, the so called gravitational Maxwell equations, Eqs. (17) and (18)
Ñ e := ¤4pGNr; Ñb := 0 (17)
Ñe := 0; Ñb := ¤
16pGN
c2 j (18)
where j = rv is the mass flux and GN is Newton’s gravitational constant. The field e describes the gravitational field
from a stationary mass distribution, whereas b describes an extra gravitational field produced by moving masses. Fig.
(4) depicts the experiment of Tajmar et al., where a superconducting ring is subjected to angular acceleration, which
should lead to a gravitophoton force. EHT makes the following predictions for the measured gravitational fields that
are attributed to photon-gravitophoton interaction.
• For the actual experiment, shown in Fig. 4 (Tajmar et al.), the gravitophoton force is in the azimuthal direction,
caused by the angular acceleration of the superconducting niobium disk. The acceleration field is opposite to the
angular acceleration, obeying some kind of Lenz rule.
• For the novel experiment of Fig. 5 (field propulsion), a force component in the vertical direction would be
generated.
It will be shown in the following that the postulated gravitophoton force completely explains the experimental facts
of the experiment by Tajmar et al., both qualitatively and quantitatively. It is well known experimentally that a rotating
superconductor generates a magnetic induction field, the so called London moment
B = ¤
2me
e
w (19)
where w is the angular velocity of the rotating ring. It should be noted that this magnetic field is produced by the
rotation of the ring, and not by a current of Cooper pairs that are moving within the ring.
Gravito-Magnetic Effect Predicted by EHT
In this short version of the paper, only the final result for the acceleration field is stated without derivation. Comparisons
of theoretical and experimental values for their most recent gravito-magneto measurements are shown below. A
coupling between electromagnetism and gravitation is basic to EHT, because of the fifth and sixth fundamental interactions,
which foresee a conversion of Hermetry form H7, describing the photon, into the Hermetry form H5, describing
the gravitophoton. The gravitophoton then, according to EHT, decays into a graviton and a quintessence particle. The
two additional interactions predicted by EHT, are identified as gravito-magnetic interaction and quintessence. The
quintessence messenger particle causes a weak repulsive gravitational like interaction, which might be identified with
dark energy.
The laboratory generation of gravity has been under active research for the last fifteen years and numerous
experiments were carried out. So far, only the experiments by Tajmar et al. have sufficient credibility. None of the
other experiments have stood the test of time, and therefore are not investigated.
Without further demonstration, the gravitophoton acceleration for the in-Ring accelerometer for as derived from
EHT is presented. It is assumed that the accelerometer is located at distance r from the origin of the coordinate system.
From Eq. (19) it can be directly seen that the magnetic induction has a z-component only. Applying Stokes law it is
clear that the gravitophoton acceleration vector lies in the r¤q plane. Because of symmetry reasons the gravitophoton
acceleration is independent of the azimuthal angle q, and thus only has a component in the circumferential (tangential)
direction, denoted by ˆeq . Since the gravitophoton acceleration is constant along a circle with radius r, integration is
over the area A = pr2 ˆez. Using the values for Nb, k and a, and carrying out the respective integration, the following
expression for the gravitophoton acceleration is eventually obtained
ggp = ¤(0:04894)2 me
mp
w˙ reˆq (20)
where it was assumed that the B field is homogeneous over the integration area.
Comparison of EHT and Gravito-Magnetic Experiments
The experiments by Tajmar are interpreted such that a conversion from photons into gravitophotons takes place as
outlined above.
For comparisons of the predictions from EHT and the gravito-magnetic experiments, the most recent experimental
values taken from the paper by Tajmar et al. [5] were used. The following values were utilized:
w˙ = 103rad=s2; r = 3:610¤2m;
me
mp
= 1=1836
ggp = ¤(0:04894)210¤43:610¤21039:81¤1g (21)
resulting in the computed value for the circumferential acceleration field
ggp = ¤4:7910¤6g (22)
For a more accurate comparison, the coupling factor 17 kgp for the in-Ring accelerometer, as defined by Tajmar, is
calculated from the value of Eq. (22), resulting in kgp =¤4:7910¤9g rad¤1s2. The measured value is kgp =¤14:4
2:810¤9g rad¤1s2. This means that the theoretical value obtained from EHT is underpredicting the measured value
by approximately a factor of 3. The agreement between the predicted gravitophoton force is reasonable but not good.
Comparisons for lead are not made, since according to Tajmar 18 these measurements [7] need to be repeated. Using
the postulated equation from Tajmar et al. [5]
ggp = ¤1=2bgprˆeq = ¤
r
r
rw˙ eˆq (23)
results in a value kgp = ¤7:1610¤9grad¤1s2.
It should be kept in mind that the present derivation from EHT does give a dependence on the density of Cooper
pairs for coupling values k and a, but, according to our current understanding, such a coupling occurs only for two
materials, namely Nb and Pb.
In [5] a second set of measurements were taken using laser gyroscopes to determine the bgp. The formula used in
this paper employing the actually measured value has the form
bgp = ¤1:9510¤6w rad s¤1 (24)
Comparing this with the equation derived from EHT, Eq. (22), it is found that the theoretical prediction is overpredicting
the measured results by a factor of 1.34, which is in good agreement with experiment. The value computed from
Eq. (23), see [5], is overpredicting the measured value by about a factor of 2.
Experiment for Gravitomagnetic Field Propulsion by Gravitophoton Acceleration
There exists a major difference between the experiment of Fig. (4) and a gravito-magnetic field propulsion device.
Present experiments only show the existence of a gravitational field as long as the ring undergoes an angular acceleration.
The artificial gravitational field is directed opposite to the applied angular acceleration, following some kind
17 This coupling factor, as defined by Tajmar [5], is the ratio of the magnitudes of observed tangential acceleration ggp and applied angular
acceleration w˙ .
18 e-mail communication February 2007
Figure 5. This experiment, derived from EHT, is fundamentally different from the experiment by Tajmar et al. in two ways.
First, EHT predicts the neutral gravitophoton to decay in a negative (attractive) and a positive (repulsive gravitophoton that is,
the physical mechanism is different. Second, the artificial gravitational field generated would be directed in the axis of rotation.
Hence, this acceleration field would be used as propulsion mechanism. In other words, this experimental setup would serve as a
demonstrator for a propellantless propulsion system. It comprises a superconducting coil and a rotating disk of a special material.
The black cylinder is meant to be the space vehicle, while the coil and the disk are the propulsion system that are mechanically
attached to the space vehicle. The acceleration field would be generated directly above the rotating disk.
of gravitational Lenz rule. For a propulsion device, however, the force must be directed along the axis of rotation,
and not in the circumferential direction of the rotating ring. Therefore, a fundamentally different experiment must be
designed to obtain a field along the axis of rotation. While the experiments by Tajmar et al. demonstrate the possibility
of generating artificial gravitational fields, emphasizing the importance of a condensed state (Cooper pairs, bosons),
a novel experiment is needed to demonstrates the feasibility of gravito-magnetic field propulsion. The experimental
setup for such a device is pictured in Fig. (5).
Two acceleration components are generated: one in the radial r direction, and the second one in the z- direction.
These components are given by
ar ˆer = vTq bz ˆeq ˆez; az ˆez =
(vTq )2
c
bz(ˆeq ˆez)ˆeq (25)
where vTq denotes the velocity of the rotating disk or ring, and bz is the component of the (gravitational) gravitophoton
field bgp (dimension 1/s) in the z-direction, see Fig. (5). In contrast to the fermion coupling, ref. [14], experimental
requirements are substantially lower.
According to our current understanding, the superconducting solenoid of special material (red), see Fig. (5), should
provide a magnetic induction field in the z direction at the location of the rotating disk (gray), made from a material
different than the solenoid. The z-component of the gravitophoton field is responsible for the gravitational field above
the disk. This experimental setup could also serve as field propulsion device, if appropriately dimensioned. Fig. (5)
describes the experimental setup utilizing a disk rotating directly above a superconducting solenoid. In the field
propulsion experiment of Fig. (5), the gravitophoton force produces a gravitational force above the disk in the zdirection
only. The following assumptions were made: N = 10, number of turns of the solenoid, current of about 1A
(needed to calculate bz), diameter of solenoid 0:18m, and vTq = 25 m/s. The disk should be directly above the solenoid
to produce a magnetic field in z-direction only. This experiment should give an acceleration field ggp = 610¤3gˆez;
which is an appreciable field acting directly above the rotating disk.
From these numbers it seems to be feasible that, if our theoretical predictions are correct, the realization of a space
propulsion device that can lift itself from the surface of the Earth is within current technology.
CONCLUSIONS AND FUTURE ACTIVITIES
It has been shown that even with an advanced fission propulsion system (most likely the only feasible device among
the advanced concepts within the next several decades), space travel will both be very limited regarding, speed, range,
and payload capability as well as cost. Travel time to other planets will remain prohibitively high. Interstellar travel is
impossible. To fundamentally overcome these limitations, novel physical laws are needed. It was also shown that the
status of current physics leaves many important questions unanswered and, concerning the role of the vacuum, severe
contradictions exist. The nature of spacetime is not clear.
On the other hand, it has been shown that the current status of both experimental and theoretical gravito-magnetic
research indicates that a novel coupling between electromagnetism and gravitation might exist, which could result in
the generation of artificial gravitational fields. Such an effect is not predicted by current physics. The experiments by
Tajmar et al. cannot be explained by the well known frame dragging effect of GR, since measured values are more
than 20 orders of magnitude larger than predicted by GR, and thus should not be visible at all in the laboratory. In
particular, these recent experiments , if confirmed, show that such an artificial gravitational field may be generated
with current technology. Therefore, the search for novel physical phenomena is both justified and necessary.
As was shown, Extended Heim Theory (EHT) predicts a coupling between electromagnetism and gravitation that
directly leads to the generation of artificial gravitational fields. Predictions of EHT were compared with experimental
data obtained from gyroscope and acceleration measurements, and satisfactory agreement with experimentaldata was
demonstrated. However, it is one thing to come up with a theory that fits the measured data. It is quite another, to
show that EHT unambiguously predicts two additional interaction that actually occur in the natural world. Therefore,
in order to confirm EHT, a novel experiment must be carried, and an artificial gravitational field along the axis of
rotation of a rotating disk needs to be produced, Finally the propellantless propulsion device must be constructed and
its working demonstrated.
In EHT, which can be considered as the natural extension of GR, matter is a consequence of the internal physical
features of spacetime and thus, with each point in spacetime, an internal symmetry space, termed H8, is associated.
In GR the metric tensor is obtained from a transformation between Cartesian and curvilinear coordinates. This
metric tensor then is associated with gravitation. In EHT, a double transformation is used involving also the internal
coordinates of the 8-dimensional space H8. Since H8 comprises four subspaces and only certain combinations of these
subspaces are admissible to obtain a metric that has physical significance, a poly-metric is constructed. Each metric
tensor is associated with an interaction or particle. According to EHT, six fundamental interactions should exist. The
two additional forces are gravitational like, but can be both attractive and repulsive. Moreover, an interaction between
electromagnetism and gravitation should exist. In particular, EHT predicts that superconductivity with a high density
of Cooper pairs is an essential part for the (boson) coupling between electromagnetism and gravitation.
The coupling constants of the interactions were obtained from number theory, and thus are calculated theoretically.
It is interesting to note that they were published in 1996 and used without modification to explain and quantitatively
compare with the experiments by Tajmar et al. EHT was used to calculate the dependence on the coupling constants
of the superconductor material, namely for lead and niobium.
Furthermore, guidelines were established by this theory to devise a novel experiment for a field propulsion device
working without propellant. In this experiment an artificial gravitational field should be generated along the axis of
the rotating disk (ring). Initial calculations show that experimental requirements are well within current technology.
Boson coupling seems to substantially alleviate experimental requirements like magnetic field and current density.
Research should focus on this experiment, because of its potential applications in the field of transportation.
The recent experiments by Tajmar et al. provide credible experimental evidence for these laws. In conjunction
with the theoretical framework of EHT, the construction of a technically feasible field propulsion device might be
achievable. This propulsion principle would be far superior compared to any device based on momentum generation
from fuel, and would also result in a much simpler, far cheaper, and much more reliable technology. Such a technology
would revolutionize the whole area of transportation.
ACKNOWLEDGMENT
The authors are most grateful to Prof. P. Dr. Dr. A. Resch, director of the Institut für Grenzgebiete der Wissenschaft
(IGW), Innsbruck, Austria for his support in writing this paper. The second authors gratefully acknowledges his
hospitality and numerous discussions being a guest scientist at IGW in 2007.
The authors are particularly grateful to Dr. M. Tajmar, ARC Seibersdorf, Austria for providing measured data as well
as discussions that helped us to perform comparisons between EHT and his experiments and also lead to corrections
of computed values.
The second author was partly funded by Arbeitsgruppe Innovative Projekte (AGIP) and by Efre (EU) at the Ministry
of Science and Education, Hannover, Germany.
The authors gratefully acknowledge the invitation by Dr. J. Longo, DLR Braunschweig, Germany to present their
results at this conference.
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