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Coupled Gravitational Fields A New Paradigm for Propulsion Science

02.05.2014 13:48

AIAA2010-021-NFF-1-heim drive.pdf (671,1 kB)

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit AIAA 2010-NFF1

25 -28 July 2010, Nashville, Tennessee

Coupled Gravitational Fields

A New Paradigm for Propulsion Science

Walter Dröscher1, Jochem Hauser 2

1Institut für Grenzgebiete der Wissenschaft, 6010 Innsbruck, Austria

2Faculty H, Ostfalia Univ. of Applied Sciences, Campus Suderburg, 29556, Germany

Current space transportation systems are based on the principle of momentum conservation of classical physics.

Therefore, all space vehicles need some kind of fuel for their operation. The basic physics underlying this propulsion

principle severely limits the specific impulse and/or available thrust. Launch capabilities from the surface

of the Earth require huge amounts of fuel. Hence, space flight, as envisaged by von Braun in the early 50s of the

last century, has not been possible due to this concept. Only with novel physical principles, providing the proper

engineering principles for propellantless propulsion, can these limits be overcome. The concept of gravitational

field propulsion represents such a novel principle, not being based on the movement of extremely large masses

(e.g., planets or stars), but by the capability of building devices for the generation of gravity-like (i.e. acceleration)

fields in a way similar to electromagnetism. In other words, gravity fields should be technically controllable.

Since a propulsion system based on gravity-like fields has to function in empty space, it has to interact with the

spacetime field itself. At present, physicists believe that there are four fundamental interactions: strong (nuclei,

short range), weak (radioactive decay, short range), electromagnetic (long range), and gravitational (long range).

As experience has shown over the last six decades, none of these physical interactions is suitable as a basis for

novel space propulsion. Furthermore, none of the advanced physical theories, like string theory or quantum

gravity, go beyond these four known interactions. On the contrary, recent results from causal dynamical triangulation

simulations indicate that wormholes in spacetime do not seem to exist, and thus, even this type of exotic

space travel appears to be impossible. However, there seems to be genuine evidence of novel physical phenomena,

based on both new theoretical concepts as well as recent experiments that may have the potential to leading to

propellantless space propulsion technology, utilizing two novel fundamental long range gravity-like fields that

should be both attractive and repulsive, resulting from the interaction of electromagnetism and gravity. The

current theoretical and experimental concepts pertaining to the physics of gravity-like fields are discussed together

with recent experiments of producing extreme gravitomagnetic fields, performed at the Austrian Institute

of Technology (AIT). The fundamental theoretical concepts termed Extended Heim Theory, EHT, are presented,

and by further applying the physical ideas of EHT, it is argued that, in contrast to the circumferential gravity-like

fields observed in the experiments at AIT, gravity-like fields acting parallel to the axis of rotation of the cryogenic

disk may be producible, which should be strong enough for propulsion purposes. The basic experimental setup

along with respective technical requirements as well as the resulting acceleration are described.

Nomenclature

gp = two types of neutral gravitophotons (gravitational gauge boson)

gp+n¤

gp = positive (attractive) and negative (repulsive) gravitophotons (gravitational gauge bosons)

ng = graviton (gravitational gauge boson, attractive)

nq = quintessence particle (gravitational gauge boson, repulsive)

wI = angular velocity of imaginary electrons

BG = gravitomagnetic field vector from real moving masses

1Senior Scientist, Institut für Grenzgebiete der Wissenschaft, 6010 Innsbruck, Austria

2 Prof., Faculty H, Ostfalia Univ. of Applied Sciences, Campus Suderburg, 29556, Germany, Senior member AIAA.

and Astronautics, Inc. with permission.

I EXPERIMENTAL AND THEORETICAL CONCEPTS OF NOVEL FIELD PROPULSION 2

Bgp = observed gravitomagnetic field vector

EG = gravitoelectric field vector from stationary masses

Egp = gravitoelectric field vector from gravitophotons

G = gravitational constant comprising three parts, GN;Ggp;Gq

GN = Newtonian gravitational constant, (mediated by graviton, attractive force)

Ggp = gravitational constant for gravitophoton interaction = 1

672GN, this type of gravitation is

both attractive and repulsive

Gq = gravitational constant of quintessence interaction, repulsive, 10¤18GN

gmn = component of metric tensor as in GR, m;n = 0;1;2;3

gmn (H`) = metric tensor of Hermetry form H`; ` = 1; :::;16

ggp = gravitophon acceleration (in contrast to gravitational acceleration by gravitons)

H8 = Heim space, eight-dimensional internal space attached to each point of spacetime

H` = Hermetry form (metric subtensor from double coordinate transformation), ` = 1; :::;16

me;mp = electron and proton mass, respectively

O(8;q) = group structure of all messenger bosons where q denotes the set of quaternions

O(8;q) = symmetry group structure of 15 Hermetry forms that describe

the physically possible particle families and fields

R3 , T1 , S2 , I2 = subspaces of internal space H8

v = circumferential velocity of disk in axial field experiment

I. Experimental and Theoretical Concepts of Novel Field Propulsion

A. Current Status of Space Propulsion

THE current status of space propulsion is characterized by two contradicting scenarios. The first one, chemical

propulsion delivers high thrust but for several minutes only at relatively low specific impulse, and is used today

to lift heavy payloads from the surface of the Earth into nearby space (for instance LEO). The second one, electric

and plasmadynamic propulsion, provides low thrust over longer periods of time (up to several months) at high specific

impulse, and is employed in scientific interplanetary missions of long duration. Propulsion systems can be classified

according to their physical principles as thermal propulsion systems or electromagnetic propulsion systems. Advanced

versions of these systems are described in the recent book by Bruno et al.,21 which performs a linear extrapolation of

present technology, envisaged to be realizable in 2020. Another class of advanced concepts using photonic propulsion,

solar sails, or laser propulsion has been suggested. Comparing these advanced concepts with the space propulsion

concepts discussed in the books by Seifert et al. (1959)1 and Corliss (1960)2 it becomes obvious that the physical

principles of all of these concepts have been around for several decades, but with regard to performance no

significant progress has been made. For instance, electric propulsion systems were already tested in the 1960s and so

was nuclear propulsion. Chemical propulsion systems were never more powerful than in the 1960s.

The reason for this lack in progress is that physical laws pose strict limits on the practicality and the performance

of even the most advanced propulsion systems and in practice have prevented the construction of efficient and effective

propulsion systems. First, all systems considered so far operate on the basis of expulsion of mass and energy, i.e.,

have to obey classical momentum conservation. Hence, some kind of propellant needs to be provided. Second, the

speed of light in vacuum is limited by special relativity, so interstellar travel in general does not seem to be feasible

in our spacetime. This, however, is not at all a concern at present, since our current chemical propulsion systems are

delivering velocities of about 10 km/s.

The state of the art of different types of advanced space propulsion concepts, based on more sophisticated physics,

like space drives, warp drives, or gravity control are described in Davis and Millis (eds.)3 . Nevertheless, these

concepts are all utilizing one of the known four fundamental physical interactions. For instance, they are making

use of special properties of the spacetime metric of general relativity (GR), or try to exploit quantum entanglement

for faster than light travel. Although these concepts have been known, too, in physics since the late 1930s, their

engineering realization seems to be as unlikely today as it was at the time of their discovery. In particular, faster than

light approaches in general relativity, GR, as investigated by Davis, Chapter 15, in3 probably are ruled out by novel

causal dynamical triangulation computer simulations4–6 , since realistic spacetime topologies do not seem to allow

this kind of traversable wormholes, and this type of interstellar travel thus appears unfeasible.

B Novel Physical Interactions and Particles 3

Figure 1. The picture shows the rapidly increasing mission difficulty and hazard of current space propulsio technology with

respect to flight distance. The abscissa depicts distance in km while the ordinate shows the travel time in days. Space flight

as envisaged by von Braun cannot be achieved within the stringent limits imposed by the currently four known fundamental

physical interactions.

B. Novel Physical Interactions and Particles

On the other hand, current physics has no explanation for the existence of exactly four fundamental forces that is,

there is a belief only about the existence of four fundamental interactions7, 8 . The question therefore arises, are there

any additional fundamental physical interactions? Perhaps it is classical physics and not quantum mechanics that is

incomplete, i.e., there might exist additional long range interactions. This question was discussed and analyzed in

more detail in several recent papers, for instance9, 14–16 . For several years, novel physical ideas have been presented

under the name Extended Heim Theory, (EHT) a by complementing spacetime with an internal eight-dimensional

space H8 . No extra spatial dimensions exist. that is, spacetime is 3+1. Although these physical concepts of EHT were

laid out in previous publications, see for instance,9, 14–16 a concise presentation for the sake of understanding of the

essential features will be given in this paper. Most important, EHT is postulating the existence of six fundamental

forces. According to EHT, there should be three gravitational forces in combination with the known electromagnetic,

weak, and strong interactions. Beside Newtonian gravitation (graviton ng attractive, coupling constant GN), EHT

requires the existence of two additional gravitational fields, termed gravitophoton interaction ngp both attractive and

repulsive, which results from the conversion of electromagnetic energy into gravitational energy, and quintessence nq,

(repulsive)9, 10, 15, 16, 48 .

The question naturally arises about the physical relevance of theses ideas. Are there any, hitherto unknown, physical

phenomena that might justify the assumption of the existence of additional physical interactions? The answer

seems to be affirmative. In March 2006, the European Space Agency (ESA), on their webpage, announced credible

experimental results, reporting on the generation of both extreme gravitomagnetic (termed frame dragging in GR,

which, however, is too small to be measured in a laboratory on Earth) and gravity-like or gravitoelectric fields, which

aIt should be noted that this doe not mean that EHT has reached the status of physical theory. At present it is a collection of novel additional physical

concepts, leading to the construction of a poly-metric tensor that possibly encompasses all physical interactions9, 14, 15 . It is a phenomenological

approach to geometrize all physical interactions as envisaged by Einstein in one of his latest papers, see20 . EHT constitutes a phenomenological

approach to classify physical interactions and physical particles, extending the idea of mono-metric from GR to poly-metric as presented by Heim22

in 1952, and Finzi32 in 1955.

C Extreme Gravitomagnetic and Gravity-Like Fields 4

are acceleration fields b, performed at AIT Seibersdorf, Austria. Since then further experimental results have been

published by Tajmar et al. at AIT34–36 . In July 2007, Graham et al. published a paper on the generation of a gravitomagnetic

field produced by a cryogenic lead (Pb) disk, but using a completely different measurement technique that

excludes any potential perturbation by mechanical vibrations,37 see also Table 4 in48 . However, their results are not

conclusive, since the sensitivity of their ring laser was about two orders of magnitude lower than the gyro employed

at AIT. In addition, in 2008 Tajmar et al.38 published a more comprehensive set of gravitomagnetic experiments.

Furthermore, in 2007 and at the end of 2008 the final results of the NASA Stanford Gravity-Probe B (GP-B) experiment19

became available. In a recent paper, EHT was used to model the large unexpected gyro anomaly seen when

this experiment was in orbit as well as the unforeseen acceleration and deceleration of the two gyro pairs, for details

see9 .

C. Extreme Gravitomagnetic and Gravity-Like Fields

GR predicts that any rotating massive body (Earth) drags its local spacetime around, called the frame dragging effect,

generating the so-called gravitomagnetic field. This effect, predicted by Lense and Thirring in 1918, however, is far

too small to be seen in a laboratory on Earth. For this reason the Gravity-Probe B (GP-B) experiment was finally

launched in 2004 after more than 40 years of preparation. In this experiment the mass of the Earth was used as a

test body and measuring time was about 10 months. Measurements proved to be extremely difficult. The results are

presented in the final report19 . On the other hand, the values measured by Tajmar et al., utilizing a small cryogenic

rotating niobium (Nb) ring, are about 18 orders of magnitude higher than predicted by GR, and therefore are outside

GR. They cannot be explained by the classical frame dragging effect of GR, and would represent a new kind of

physical phenomenon. In other words, the cryogenic Nb ring in the laboratory of a mass of about 400 grams is

causing approximately the same gravitomagnetic effect as a white dwarf 9 . In this context, it is highly interesting

to compare this scenario with the so called dipole gravitational field generator, first conceived by R. Forward, and

recently described by Davis, see Chapter 4 of3 . Instead of an electric current, Forward used a mass flow together with

the Lense-Thirring effect, to produce a gravitomagnetic field Bg. He showed that the mass of a white dwarf needs to

be rotated to obtain an appreciable effect. From an engineering standpoint, his concept it totally unrealistic. However,

compared with the recent experimental results of Tajmar, a Tajmar-Forward dipole gravitational field generator

would invalidate these conclusions. Therefore, if the experiments by Tajmar et al. are correct, their physical roots

must be outside GR, and thus would support the prediction of EHT about the existence of additional long range force

fields. In these experiments there seems to occur an effect that increases the gravitational permeability of the vacuum,

16pGg=c2, by many orders of magnitude. The control parameter is temperature T, and a phase transition seems to

occur at a certain, material dependent, critical temperature TC, not necessarily identical with the formation of Cooper

pairs, which are formed at the onset of superconductivity.

When analyzing the experiments by Tajmar et al., it became clear that though the gravitomagnetic Bgp and gravitoelectric

Egp fields (the subscript gp is used to indicate that gravitophotons are deemed responsible for these extreme

gravitomagnetic fields) are huge compared to the effects predicted by GR, they are quite small when compared to

the forces needed for a space propulsion system. Also, since the gravitoelectric acceleration in Tajmar’s experiments

produced by the accelerated rotating cryogenic ring lies in the plane of the ring, i.e., in the circumferential direction, it

cannot be directly used to accelerate a space vehicle. To this end, a force along the axis of rotation is needed. Therefore,

though the AIT experiments seem to predict novel physics, and thus are of prime importance, their relevance for a

gravity-engineered technology may be less pronounced. Moreover, for a space propulsion system or for the alternative

generation of energy, a force acting in the axial direction without requiring the ring to be accelerated or decelerated

is much more advantageous.

Since this novel effect only occurs at cryogenic temperatures, it is surmised that a phase change takes place.

Moreover, EHT postulates that this phase change is leading to novel kind of particles. These virtual particles are

identified as electrons of imaginary mass denoted by eI , see Fig. 3. The coupling mechanism taking place at low

temperature for these imaginary electrons is thought to lead to bosons, similar to the formation of Cooper pairs by real

electrons in the superconducting phase. This process should lead to some kind of Bose-Einstein condensate, requiring,

however, a conversion process that eventually is producing a force of gravitational nature.

According to EHT, with regard to the construction of an advanced propulsion device, a genuine base experiment

should be feasible, in which the gravity-like field (acceleration field) is directed along the axis of rotation, and thus

could provide the required direct mechanism for a field propulsion principle working without propellant. In addition,

bIn analogy to electromagnetism, gravity-like fields are denoted as gravitoelectric fields EG since they actually produce an acceleration. One

speaks of a gravitoelectric force if the EG field is generated by stationary masses. The term gravitomagnetic force is used if EG = vBG , i.e.

produced by a rotating mass together with a mass density current.

D Propellantless Space Propulsion 5

it is argued that the experiment can be scaled such that a propulsion system can be constructed to lift a sizable mass

from the surface of the Earth. EHT will be employed to providing guidelines for the setup of this experiment and

calculating the technical requirements for magnetic induction field strength, current density, and supply power. The

numbers obtained should be realizable with present technology.

D. Propellantless Space Propulsion

Naturally, a propulsion system based on the generation of gravity-like fields, i.e., working without propellant, would

be far superior over any existing propulsion technology, while its base technology might be substantially simpler

and cleaner than chemical, fission, or fusion rockets. Such a system has to work in empty space and therefore, for

the requirements from energy and momentum conservation, needs to interact with the spacetime field itself, i.e.,

any analysis based on the conservation principles has to consider the physical system formed by the space vehicle

and its surrounding spacetime. This topic is discussed in more detail in Sec. III. There is, of course, insufficient

knowledge at present, both theoretical and experimental, to guarantee the realization of such a device, but there is

sufficient evidence both from experiment and theory to invest in the design and prototype construction of a device

for generating an axial gravity-like field.

II. Types of Matter

The two additional gravitational fundamental forces are supposed to be mediated by gravitophotons (attractive,

gp and repulsive, n¤

gp) as well as the quintessence particle (repulsive, nq, dark energy). The quintessence particle,

nq, is assumed to be responsible for the interaction between the spacetime field (vacuum field) and ordinary matter.

Regarding Fig. 3, the outer cube, that contains non-ordinary matter (NOM), shows that there should exist the

imaginary electron eI . Comparison with the corresponding Hermetry form H6 of charged leptons for ordinary matter

(OM) shows that subspace R3 is missing in the metric tensor of this Hermetry form, which is considered to be responsible

for the existence of particles with real mass, for details see10 and48 . The presence of R3 (cardinal number 3)

in a Hermetry form therefore seems to be necessary for the existence of the various types of real matter. Subspace

T1 (cardinal number 1) is deemed to be necessary for charged particles in conjunction with the proper Higgs field.

Subspace dimensions may also play a role in computing the coupling constants (set algebra). The Hermetry form that

describes neutral leptons, e0;m0; t0, which belong to NOM, could also be of importance. Since these particles do

not carry any electric charge they are not subject to electromagnetic interaction, and thus cannot decay in the same

way through the weak interaction as their charged counterparts, and hence might be stable but invisible. Their masses

could be close to those of the charged leptons. Thus, they could be candidates for dark matter. Their interaction with

ordinary matter should be mediated through gravitophotons. However, there is also an alternative, termed imaginary

matter, that we favor, and which is discussed in the following section.

A. Imaginary Matter

The concept of imaginary matter , i.e. particles that possess imaginary mass but otherwise have the same properties

as their real counterparts, should be understood as if there existed a type of matter which is of immaterial character.

This means, imaginary matter cannot be weighed (i.e. does not carry weight in our spacetime), but nevertheless its

presence in spacetime can be felt through its interaction with ordinary matter.

At present we favor the idea that dark matter is comprised of imaginary matter, see Sec. IV. In EHT, since dark

matter is believed to be composed of particles of imaginary mass, their presence should be perceptible in spacetime

through gravitational interaction with ordinary matter. In this regard, dark matter should not be directly observable.

It is unlikely that dark matter is comprised of WIMPS (Weakly Interacting Massive Particles) whose masses are

supposed to be hundreds of GeV, and thus have elucidated present accelerators. In EHT, dark matter interaction occurs

through the gravitophoton field with coupling strength Ggp. The coupling between dark matter and ordinary matter

should be given by

GNGgp = 1=67GN.

In EHT, the set of Hermetry forms leads not only to six gravitational bosons, but also to three different types of

photons, namely g, responsible for electromagnetism, gI the interaction boson among imaginary charged particles, and

gIR which conveys the interaction between charged particles of ordinary and imaginary matter. The three gravitational

interactions, should be mediated by the six interaction bosons that is, two neutral gravitophotons, the attractive and

repulsive gravitophotons as well as the graviton (Newtonian gravitation), and the quintessence particle (repulsive,

A Imaginary Matter 6

dark energy), see Fig. 2. Here, we only note that in EHT the symmetry group for all messenger bosons is

O(8;q) = SU(4)gl SU(2)emSU(2)wSU(2)gqSU(2)gpU(1) (1)

where q denotes the set of quaternions. For the present discussion it may suffice to say that the first group on the

right hand side defines the 8 gluons of the strong interaction, one gluon for imaginary masses, and six gluons that

are responsible for interaction between real and imaginary baryons , the next group stands for the three types of

photons, g; gI ; gIR that is for the complete electromagnetic interaction. The next group describes the three well known

vector bosons of the weak interaction. The following two groups are unknown in current physics, since the first one

describes the gravitational bosons responsible for the axial field, n01

gp, n+

gp, and n¤

gp, while Tajmar’s experiments

would be given by n01

gp, ng, and nq. The last group, having only one generator is responsible for the inertia of matter,

i.e. it is some kind of all pervading Higgs field. However, it should be noted that EHT postulates a total of six

Higgs and anti-Higgs fields. This topic will be discussed in much more detail in the forthcoming review paper11

. Particles of imaginary mass should also occur as virtual particles, which means that they are not present (do not

occur) in the initial and final states of a reaction, but act in the intermediate steps. They might be conceived as a

catalyst, enabling a novel physical interaction, namely the conversion of electromagnetic into gravitational fields as

might have taken place in the recent gravitomagnetic experiments. This means that all observed particle masses and

charges are still real, being the endproducts of a reaction. The neutral gravitophotons, n01

gp and n02

gp should decay into

two different ways, Fig.2 . The first one, in which the n01

gp decay results in positive and negative gravitophotons, should

produce a vertical (axial) gravity-like field by inducing an imaginary electric current in the cryogenic rotating disk

(at constant angular frequency) c. Eventually this imaginary current, which is interacting with the imaginary vector

potential from the superconducting coil below the disk, is converted into a real gravity-like field, see the description

in Sec. IV. The second decay scheme, giving a graviton and a quintessence particle, is assumed to take place in

the experiments by Tajmar et al., when a circumferential gravity-like field in the plane of the ring is produced by

mechanically accelerating the cryogenic Nb ring. The time dependent angular frequency is considered to be the cause

of the decay of n02

gp, responsible of the strong gravity-like field measured by Tajmar et al. In any case, the extreme

gravitational fields seem to be of electromagnetic origin. Furthermore, an interaction with spacetime (physical field)

needs to be assumed to account for conservation of momentum and energy, Sec. III.

Figure 2. Hermetry form H9 stands for the neutral gravitophoton, ngp, produced by photon conversion, which can decay via two different

channels, depending on experimental conditions. It should be noted that there are two neutral gravitophotons, denoted in the text by n01

and n02

gp. In the picture, for the sake of simplicity, only one neutral gravitophoton is shown. The first one, upper branch, seems to take

place in the generation of the axial (vertical) acceleration field, called the Heim experiment. The second branch is assumed to occur in the

gravitomagnetic experiments by Tajmar et al. and Graham et al.

Moreover, there should be neutral leptons, with inertial masses of e0;m0; t0 that are assumed to be close to their

charged counterparts, i.e., 0:511 MeV/c2 for electrons, 105:66 MeV/c2, and 1:78 GeV/c2 (compared to 938 MeV/c2

for protons). If e0;m0; t0 existed in Nature, the question naturally arises: why did not accelerators already long ago

produce these particles? Accelerators or colliders produce beams of high-energy electrons or protons that are driven

onto a target, or two beams are colliding from opposite directions. For some unknown reason these leptons seem not

to be produced in high energy collisions. In the Standard Model, there is no place for OM neutral leptons, except for

the neutrinos, which, because of the experimentally established bounds on their masses, cannot contribute more than

1 % to dark matter. In EHT, the NOM counterpart to neutrinos actually are the neutral leptons e0;m0; t0.

cTajmar et al. use a ring geometry, Graham et al. were using a disk, which will also be used in the proposed Heim experiment.

A Imaginary Matter 7

Figure 3. In EHT, derived from the concept of internal space H8 , there exist two types of matter, ordinary matter (OM) (inner cube)

and non-ordinary matter (NOM) (outer cube). In present physics, NOM does not exist. Each cube represents eight Hermetry forms. A

Hermetry form stands for a family of particles, that in turn is represented by its own symmetry group. In this regard there is not a single

supergroup structure that contains all forces and particles. Instead a hierarchy of groups seems to exist. The hypercube has symmetry

group O(8;q) = O(3;q)H O(2;q)h+ O(2;q)h¤ O(1;q)in where q stands for the set of quaternions. The separation of O(8;q) into four

subgroups reflects the subspace structure of Heim space H8 . Group O(3;q)H has 15 generators that represent 15 Hermetry forms, while

Hermetry form 16 is given by group O(1;q)in, the inertia field that pervades the Universe. Groups O(2;q)h+ and O(2;q)h¤ are (presently)

interpreted as six Higgs and anti Higgs fields that provide mass and charge to all particles in our Universe. NOM also contains matter of

imaginary type that is, dark matter is believed to be comprised of imaginary quarks, and hence should not be visible in our Universe, but

its presence should be felt in our spacetime by their gravitational and electromagnetic interaction with OM, see text for further description.

Thus the four-dimensional hypercube should represent all forms of matter that can impact physical events in our Universe. It should be

noted that the introduction of internal space H8 along with its sub-space structure entirely fixes the structure of the symmetry groups, and

thus determines the existence of particles as well as their interactions.

B Interaction of Electromagnetism with Gravitation at Low Temperatures 8

In order to construct the physically meaningful set of metric sub-tensors that is, the so called Hermetry forms (the

term Hermetry, coined by Heim in 1952, is referring to the physical meaning of geometry, and is a combination of

the two words hermeneutics and geometry) , it is postulated that coordinates of internal spaces S2 (organization

coordinates) or I2 (information coordinates) must be present in any metric sub-tensor to generate a Hermetry

form, whose concept was first introduced in22 . 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 occurring in NOM, namely the families of imaginary messenger particles, i.e. photon,

gluon, and dark matter, see the outer cube of the 4D hypercube in Fig.3. Hermetry form 16 is reserved for the inertia

field, which is some kind of Higgs field pervading the whole Universe. The interpretation of the meaning of Hermetry

forms was already given in Tables 1-4 of Dröscher et al.16 , but has somewaht changed since then, based on new

physical facts derived from the interpretation of the experiments by Tajmar et al.,10,48 and14 .

Because of the double coordinate transformation underlying the construction of the basic polymetric tensor from

which all Hermetry forms are constructed, see for instance16, 46 , any metric tensor describing a Hermetry form is

composed of a partial sum of metric terms, selected from the 64 components that comprise the complete polymetric

tensor, which results from the internal space H8 .

If space H8 is omitted, EHT is reduced to GR, and only gravitation remains. It is obvious that a double coordinate

transformation as employed in14 does not change, for instance, the curvature of a surface, since it is an invariant

(intrinsic to the surface). However, this fact is not relevant in the construction process of the polymetric. The physical

reason for the double transformation is to provide spacetime with the additional degrees of freedom, expressed by the

individual components of the metric tensor from which the various Hermetry forms are constructed.

Only metric tensors representing Hermetry forms are of physical relevance, and it is clear from their construction

principle that all these tensors, derived from the underlying polymetric tensor, are different. Consequently, their

respective Gaussian curvatures, K`, where ` denotes the index of the corresponding Hermetry form, must also be

different. This is straightforward to observe, since Gaussian curvature is only a function of the first fundamental

form (metric tensor components) as well as their first and second derivatives, but does not depend on the second

fundamental form. Therefore, each Hermetry form H` determines its proper Gaussian curvature K`, and thus curves

space according to its own specific metric. Having established the qualitative physical relationship between Hermetry

forms and spacetime curvature, all physical interactions are connected to spacetime curvature, similar to GR, and

thus physics has been geometrized d. Some additional remarks between the connection of geometry and physics are

in place. Internal coordinates of subspace R3 of Heim space H8 have dimension of length, and via the Compton

wave length are connected to mass, and the internal coordinate of space T1 is responsible for charge. In16 it was

already shown that spacetime must be quantized at about the Planck length scale (maybe the length scale is somewhat

larger). Moreover, it is well known that in the case of gravitation in the Newtonian limit, metric element g00 (time has

coordinate index 0 in spacetime coordinates) is proportional to the gravitational potential equation.

B. Interaction of Electromagnetism with Gravitation at Low Temperatures

There seems to be substantial evidence of novel gravitational phenomena, based on both new theoretical concepts as

well as recent experiments by Tajmar et al. at AIT, Austria that may have the potential to leading to advanced space

propulsion technology, utilizing two novel fundamental force fields. According to EHT these forces are represented

by two additional long range gravity-like force fields that would be both attractive and repulsive, resulting from interaction

of electromagnetism with gravity. At high temperature, only ordinary matter (OM) exists. At very high

temperatures, a unification of the physical interaction fields of all known forces might take place. However, at very

low temperatures, a phase transition seems to occur which is generating non-ordinary matter (e.g. virtual particles of

imaginary mass via the Higgs mechanism), causing an interaction between electromagnetism and gravitation. Hence,

additional strong gravity-like fields may result from this conversion, being both attractive and repulsive that are coupled

at these very low temperatures. It is assumed that symmetry breaking not only occurs when going from very

high to lower temperatures, but also from lower temperatures to very low temperatures (starting at about 15 K), and a

conversion of electromagnetism into gravity-like fields may occur.

III. Conservation Principles and the Spacetime Field

The rocket principle requires that momentum is taken from the fuel and transferred to the space vehicle. This means

the physical system to be considered for momentum conservation comprises the rocket and the ejected fuel masses.

dIn addition, it is assumed that color and weak charges are mediated by their Higgs bosons.

III CONSERVATION PRINCIPLES AND THE SPACETIME FIELD 9

The limits of this principle are too well known and cannot be overcome by technical refinement or by selecting more

energetic fuel. Therefore only propellantless propulsion can be the alternative. Since conservation principles for

energy and momentum must hold in all physical processes, because they represent fundamental symmetries of our

spacetime, the question arises how propulsion without fuel might be physically conceivable. There seems to be only a

single alternative.

According to EHT, the space vehicle is acquiring velocity by imparting an equal and opposite momentum to

the spacetime field. There is also the possibility that one of the six Higgs fields pervading the Universe might be

involved. Since the Higgs fields seem to confer special physical quantities (mass to hitherto massless particles, inertia,

or electrical charge etc.) it is therefore assumed that interaction takes place with spacetime. Spacetime as a physical

field carries momentum and energy. In case the space vehicle (or any other physical entity) is interacting with the

spacetime field, the physical system to be considered for energy and momentum conservation needs to incorporate

spacetime as an active partner. The momentum scale of the space vehicle is minuscule compared to that of the

spacetime of the Universe, and thus the recoil kinetic energy and momentum that spacetime is receiving from the

vehicle are almost negligible. Since momentum must be conserved, however, the exact momentum balance must

include the momentum transferred to the spacetime field. Hence, the expansion of the Universe, at least in principle,

must accelerate, although this contribution is exceedingly small and clearly cannot be measured. There may be other

processes on the cosmic scale that may, however, have an observable effect. In any case, the accelerated expansion

of the Universe seems to be caused by the principle of momentum conservation.

According to EHT, the mediators of this effect are the gravitophotons and the quintessence particle through the

formation of imaginary matter. It is obvious that this principle is applicable to any other type of transportation as long

as an interaction with spacetime can be established. The interpretation of the experiments by Tajmar et al. (in short

Tajmar effect) by EHT leads exactly to this conclusion. Furthermore, the Heim experiment for the axial gravity-like

field proposed in Sec. IV requires the existence of the gravitophotons as shown in Fig. 2. If the Tajmar effect (both,

extreme gravitomagnetic field as well as circumferential gravity-like field) can be confirmed, there is some confidence

that the Heim effect (axial gravity-like field) also might exist.

A simple analogy is used to differentiate between the classical rocket principle (including all other means of

propulsion) and the novel field propulsion concept of EHT incorporating spacetime as a physical quantity. Suppose a

boat is in the middle of a large lake or ocean. In order to set the boat in motion, a force must be mediated to the boat.

The classical momentum principle requires that a person in the boat is throwing, for instance, bricks in the opposite

direction to push the boat forward. However, everybody is well aware of the fact that there is a much better propulsion

mechanism available. Instead of loading the boat with bricks, it is supplied with sculls, and by rowing strongly the boat

can be kept moving as long as rowing continues. The important point is that the medium itself is being utilized, i.e.,

the water of the lake or ocean, which amounts to a completely different physical mechanism. The rower transfers

a tiny amount of momentum to the medium, but the boat experiences a substantial amount of momentum to make it

move. For space propulsion the medium is spacetime itself. Thus, if momentum can be transferred to spacetime

by field propulsion, a repulsive or recoil force would be acting on the space vehicle moving it through the medium,

like a rowing boat. The medium, spacetime, is a physical quantity, namely a field, and if properly quantized, the

respective particles mediating forces should also be present. Thus, in principle, spacetime should have the capability

to interact with a space vehicle. If this effect somehow can be experimentally established, the principles of momentum

and energy conservation require that the combined system, i.e., both spacetime and space vehicle, are considered.

According to EHT, this actually is the physical mechanism occurring in the experiments by Tajmar et al. and Graham

et al. Important to note, this mechanism does not extract momentum from the spacetime field and transfers it to the

space vehicle. Instead, an active process has to be triggered for the creation of gravitophotons, i.e., first generating a

strong gravitomagnetic field, Bgp. Second, in order to produce the gravity-like field seen in the experiments at AIT,

experimental conditions have to be such that the Bgp field can decay, producing gravitons and quintessence particles.

The important point is that in this scheme not only gravitons exist, but also gravitophotons as well as quintessence

particles. In the generation of the gravitomagnetic force via the decay of the gravitophoton, as is assumed to be the

case in the gravity-like experiments by Tajmar et al., both the OM (graviton, negative gravitational energy density)

and NOM (quintessence particle, positive gravitational energy density) should be generated, see Figure 2. The total

energy in the generation of these two particles is therefore zero. Gravitons interact with the space vehicle, i.e. they

are absorbed by the space vehicle, while the quintessence particles are reabsorbed by spacetime itself. This effect

causes an acceleration of the space vehicle, while the momentum of the quintessence particle is not felt by the space

vehicle, but by the surrounding spacetime and leads to its expansion, because of the repulsive force, and thus total

momentum is being conserved. This effect is most likely too small to be observed, but this kind of space propulsion

should contribute to the expansion of the Universe. In the same way the momentum change of the ocean would not be

IV HEIM EXPERIMENT: TECHNOLOGY FOR PROPELLANTLESS SPACE PROPULSION 10

discernible from the presence of a rowing boat. Perhaps a local disturbance of spacetime might be measurable in the

experiments by Tajmar et al.?

In the Heim experiment (vertical gravity-like field) the neutral gravitophoton, n01

gp, decays into the positive (attractive),

ngp+, and negative (repulsive), n¤

gp, gravitophotons, Figure 2, which follows from the construction of the set of

Hermetry forms that, in turn, are a direct consequence of internal Heim space and its separation into four subspaces.

Again, it is assumed that the negative gravitophotons act on the spacecraft and the positive gravitophotons act on space

such that total momentum is conserved. As long as the experimental conditions for the production of gravitophotons

along with their respective decay are maintained, the proper acceleration field will be generated. During this period

of time the interaction between space vehicle and surrounding spacetime remains. As soon as the gravitophoton

production and its subsequent decay stop, the acceleration field ceases to exist.

For field propulsion to work without propellant there needs to be an active physical interaction with spacetime.

The rocket principle is only concerned with the energy and momentum balance of the physical system comprising the

space vehicle and its fuel. Therefore, regardless of the technology employed, this system is bound by the momentum

that can be extracted from the stored fuel. Therefore this principle, by definition, cannot produce a viable propulsion

system delivering high speed, long range, or high payload ratio.

An interesting question remains, namely under which conditions the production of gravitophotons on the cosmological

scale can take place and how this production could have influenced the expansion of the Universe?

IV. Heim Experiment: Technology for Propellantless Space Propulsion

Tajmar et al. were the first reporting the generation of extreme gravitomagnetic fields in the laboratory, which in

EHT are denoted as Bgp since they are assumed to result from gravitophotons and not from gravitonse. It should be

noted that the existence of these fields was postulated by the authors before these experiments became known, see for

instance45 that is, theory and experiments were developed independently of each other.

Modanese et al.18 have tried to explain the Tajmar effect by employing the linear Einstein-Maxwell equations,

but have come to the same conclusions as the authors, namely that these equations do not even reproduce the correct

sign of the gravity-like field (acceleration field) that was observed by Tajmar et al. when the angular frequency of

the cryogenic ring was subject to change, i.e. the ring was accelerated. The other problem of course is that the Bgp

field measured is up to 18 orders of magnitude larger than predicted by GR. Without further discussion, it should be

mentioned that the often cited ratio of the gravitational and the electromagnetic force, which for proton and anti-proton

is in the range of 10¤36, can no longer be used to justify the negligibility of gravitational effects. This value only holds

for Newtonian gravitation.

The observed gravity-like field follows a Lenz type rule, i.e., it is opposing its origin. This exhibits an electromagnetic

behavior and contradicts the sign of the Einstein-Maxwell equations. The use of the non-linear equations

of GR cannot change this picture, since the gravitational fields observed are weak enough to fully justify the linear

approximation.

The Tajmar effect cannot be explained from GR, which becomes clear in comparing the GP-B experiment with

Tajmar’s experiments. In GP-B, which was orbiting the Earth for more than 10 months at an altitude of about 640

km, the predicted Lense-Thirring precession of the gyro spin axis (inertial frame dragging by the rotation of the mass

of the Earth) , initially pointing at a guide star (locked by a telescope), is some 42 milli-arc seconds/year. This value

is small compared to the already tiny geodetic effect (spacetime curvature caused by the mass of the Earth) of 6.6

arc seconds/year. The geodetic precession occurs in the orbital plane of the satellite, while the Lense-Thirring effect

causes a precession of the gyro spin axis in the same direction the Earth is rotating (the gyro is assumed to be initially

in free fall along the axis of rotation of the Earth). For the GP-B experiment an inertial frame was required with nongravitational

acceleration less than 10¤13 m/s2. Compared to Tajmar’s equipment, his gyroscopes definitely are not

capable to detect accelerations that small. One of the major challenges of the GP-B experiment was to provide such a

drag-free (weightless) satellite. It is therefore impossible that Tajmar has observed any effect related to GR. His

effect must therefore be outside GR, pointing to a new class of gravitational phenomena, provided, of course, that

his measurements are correct. This is an indication that the standard picture of gravity as manifested in Einstein’s

1915 GR does need an extension that goes beyond the picture of gravity of simply being the result of the curvature

of four-dimensional spacetime. Therefore, the two additional gravitational fields as postulated in EHT, represented by

gravitophotons and the quintessence particle, are at least qualitatively supported. In other words, the nature of gravity

is more complex than represented by GR. All predictions of GR are correct, but it seems that it is GR which is not

complete instead of QM (quantum mechanics). Moreover, the geodetic and Lense-Thirring effects show that an

eThe gravitons from GR will not result in a gravitomagnetic field measurable in the laboratory.

IV HEIM EXPERIMENT: TECHNOLOGY FOR PROPELLANTLESS SPACE PROPULSION 11

interaction between spacetime and massive bodies exist. This whould mean that the Tajmar effect, being many orders

of magnitude larger, should have a much stronger interaction with its surrounding spacetime. This is exactly what is

needed for propellantless propulsion, which can only work if there is an intense exchange of energy and momentum

among space vehicle and spacetime, see the discussion in Sec. III .

In order to explain the Tajmar effect, an additional assumption has to be made in order to characterize the phase

transition that obviously seems to accompany all extreme gravitomagnetic phenomena. As known from superconductivity

the heuristic London equations, representing the material equations, in combination with the Maxwell equations

are essential to calculate both the qualitative and quantitative aspects of superconductivity in a heuristic way.

Therefore, from a physical point of view it is clear that the Einstein-Maxwell equations alone cannot describe

the gravitomagnetic experiments of Tajmar, in the same way the Maxwell equations cannot account for the phenomenon

of superconductivity.

• The magnitude of the extreme gravitomagnetic field points to an electromagnetic origin, being the only other

long range field with sufficient coupling strength.

• Again, the London equations will be employed. Moreover, there should be a physical mechanism that converts

an electromagnetic into a gravitomagnetic (or gravity-like) field.

• Such a mechanism is not conceivable within the framework of the four fundamental interactions which cannot

incorporate additional gravitational fields along with their additional interaction bosons. The standard model

cannot accommodate these additional particles and thus needs to be extended.

• For energy and momentum to be conserved, the interaction of the matter of the rotating disk (ring) with the

surrounding spacetime field must be accounted for.

• In the Tajmar experiments the gravity-like field of the accelerated ring is acting in the plane of the rotating ring,

opposing its origin. In the proposed Heim experiment, the gravity-like field of the disk, rotating at constant

angular velocity, is calculated to be directed along the axis of rotation. Therefore, these two experiments seem

to be based on two different physical mechanisms as depicted in Fig. 2.

• The first neutral gravitophoton, indicated by n01

gp, which is deemed to be responsible for the Heim effect, should

decay into the positive (attractive) n+

gp and negative (repulsive) n¤

gp. The resulting gravity-like field is pointing

in axial direction.

• The second neutral gravitophoton, indicated by n02

gp decays only if the ring is being accelerated, and the resulting

gravity-like field is in circumferential direction, and thus this decay route is believed to occur in the experiments

by Tajmar et al., denoted as Tajmar effect.

• From a technological point of view the axial gravity-like field is the one that could provide the enabling technologies

for propellantless propulsion and novel air and land transportation systems as well as green energy

generation etc. At present, it does not seem possible to fully assess the technological consequences of the

existence of such a field.

• The two experiments for circumferential and axial gravity-like fields are fundamentally different, but in both

cases a conversion from electromagnetic to gravitational fields seems to take place, triggered by the generation

of imaginary electrons, see NOM cube in the 4D hypercube of Fig. 3.

In the framework of the current paper a full discussion of the implications of imaginary matter cannot be given, but

the basic facts of the conversion mechanism will be presented. It seems that not only particles and their anti-particles,

but, under certain conditions, also particles and their ghost or shadow particles (i.e. imaginary mass) particles

exist, or, at least, can be created under special experimental conditions. At temperatures low enough for the respective

phase transition to occur, it seems that the imaginary electrons being produced are forming bosons comprising six

imaginary electrons eI . The imaginary current due to these sextets is deemed to result in an imaginary vector potential

AI whose interaction with the imaginary quarks qI (protons) in the rotating disk is eventually leading to a real physical

interaction which appears in the form of gravity-like fields. The physical mechanism is complex, but, as can be seen

from the experimental setup of Tajmar et al., the generation of the circumferential gravity-like field is surprisingly

simple. The same should hold true for the axial gravity-like field experiment. Any propellantless space propulsion

technology therefore would be substantially simpler and efficient than currently used chemical propulsion, and also

inherently safer as well as far more economical.

IV HEIM EXPERIMENT: TECHNOLOGY FOR PROPELLANTLESS SPACE PROPULSION 12

The experiment for the axial field comprises a cryogenic disk comprised of a given material, denoted as MD having

a diameter of about 0.2 m, rotating at circumferential velocity v. Below the disk a superconducting coil is placed,

made of material MC, that comprises N turns. The disk may also reside inside the coil. It should be noted that disk and

coil material need to be complementary. In the experiments by Tajmar et al. a Nb ring and an Al sample holder seem

to give the best results. The third part is a simple device to ensure that the current of imaginary electrons is coupled

into the coil. In order to achieve this the wire of the coil is cut through and a non-superconducting disk of about 1 mm

thickness is introduced. The Cooper pairs cannot tunnel through this layer, since its thickness far exceeds the 10 °A of

the Josephson effect. However, the Compton wave length of the imaginary electrons is much larger, because of the

small limit velocity cI in solids for particles of imaginary mass, and thus the eI should be capable of tunneling through,

leading to the imaginary current II that gives rise to the imaginary vector potential AI

In the following, the main steps for calculating the axial field strength are presented. In electrodynamics, given

a current distribution with current density (moving charges) j(x), the force on this current distribution due to the

magnetic induction B is

F =

j(x)B(x)d3x: (2)

In GR the same formula holds for calculating the gravitomagnetic Lorentz force, replacing the current density by the

mass flux density j(x) = rmv where rm is mass density, v(x) velocity of the moving mass, and Bg now denotes the

gravitomagnetic field as derived from GR. It should be noted that sometimes the vector r instead of x is used. In

any case d3x indicates the three-dimensional volume element independent of the coordinate system chosen. The electromagnetic

Lorentz force does not follow from the Maxwell equations, but has to be postulated from the Lagrange

function specifying the coupling of an electric charge to the vector potential, i.e. L = qv A. However, in the gravitational

case, the Lorentz force law follows from the geodesic equation describing the motion of a test particle in a

gravitational field. From the Lageos satellites and the GP-B experiment we know this to be true for gravitomagnetic

fields Bg resulting from large rotating masses, as given in Eq. (3 ). We assume that Eq. (2 ) holds for all gravitational

interactions, independent of the origin of the gravitomagnetic field, i.e., it should not make any difference whether

this field is produced by gravitons or gravitophotons that is, for the Bgp field.

According to GR, a material rotating spheroidal body of angular momentum J =

rmrv d3x is generating a

gravitomagnetic field Bg, where v = w r is the circumferential velocity and d3x denotes the volume element. The

subscript g indicates that this gravitomagnetic field is due to Newtonian gravitation

Bg = 2

J¤3(J ˆer)ˆer

r3 : (3)

If we insert this expression into Eq. (2), the resulting force on a moving mass distribution is found. For instance, the

force as well as the torque on a a rotating gyro can be determined that is, because of the torque, the gyro will start to

precess, or, in other words, the gyro is dragged. This can also be interpreted such that the inertial frame of the gyro is

dragged, of which the gyro defines one of the axes.

However, the gravitomagnetic mechanism of GR clearly is not the mechanism that occurs in the experiments

by Tajmar et al. As the experiments demonstrate, the process is a solid state phenomenon, depending on a phase

transition, triggered by temperature. Therefore, the generation of the gravitomagnetic field follows a totally different

mechanism different than GR. Hence, the gravitomagnetic field denoted Bgp must be calculated by a different physical

model. According to EHT,

• the gravitomagnetic field Bgp is generated by new types of bosons, termed gravitophotons n

gp,

• the origin of the Bgp is the electromagnetic field,

• conversion from electromagnetism to gravitomagnetism seems to follow the reaction chain g ! gIR ! gI !

n01

gp !n+

gp+n¤

gp!ng+nq ,

• the ng gravitophoton confers the momentum to the space vehicle, the nq gravitophoton provides negative momentum

to the surrounding spacetime which therefore expands, the total momentum of the physical system

remains unchanged, i.e. zero.

As additional material equations for gravitophoton interaction, in analogy to superconductivity, the London equations

are employed in determining the magnitude of the Bgp field in conjunction with the conversion mechanism, i.e.

fIt is not known if the direct imaginary current is superimposed by a high frequency alternating imaginary current as observed for Cooper pairs

in the Josephson effect.

IV HEIM EXPERIMENT: TECHNOLOGY FOR PROPELLANTLESS SPACE PROPULSION 13

its magnitude is determined by the underlying physics of the conversion process. It is well known that in the superconducting

case a real super current is generated by electron Cooper pairs, formed by a phase transition at critical

temperature TC, described by the heuristic London equation

B = ¤

2me

w (4)

where B is the magnetic induction field caused by the Cooper pairs. In the experiments by Tajmar et al., as discussed

in Sec. I , an extreme gravitomagnetic field is generated. For the explanation of these experimental results as well

as for the Heim experiment, it is assumed that the current of the superconducting electrons (Cooper pairs) causes a

current of imaginary electrons. Imaginary particles are formed via the Higgs mechanism, for instance, as described by

M. Kaku, Chap.1023 , further details are also given in48 . Due to the interaction of the imaginary particles with OM,

they should not behave like tachyons. For the Heim experiment, the imaginary current needs to be coupled into the

superconducting coil by some kind of tunnel effect as stated above. The Cooper pair current is not important by itself,

it only acts as the source for the accompanying imaginary current

BeI = ¤i

paI

6me

wI (5)

where wI denotes the angular frequency of the imaginary bosons formed by the coupling of the eI . Finally the conversion

of the imaginary mass meI into real mass me takes place g via the conversion from electromagnetic into gravitational

fields. Therefore, the real values are already used in the above equation. It is important to ensure experimentally

that an imaginary current is flowing in the coil, i.e. an experimental mechanism must be provided to couple this current

into the coil, once the real super-current sets in. It should be mentioned that the chain of formation of the three types

of photons g !gI !n01

gp takes only place below a certain critical temperature.

The value of the coupling constant aI

228

is related to the radiation correction of the Higgs field, see M. Kaku23

p.353, via

l aI . The factor 6meI is obtained when an imaginary instead of a real mass is considered.

The total Lagrange density for the conversion from electromagnetism to gravitation is assumed to be L = 0 that is,

i aIe+v AeI +mpv Agp = 0 (6)

where v is the velocity of the rotating disk above the coil. The decay of the neutral gravitophoton of the first type,

n01

gp, into n01

gp ! n+

gp +n¤

gp leads to the real gravitophoton potential Agp. It is assumed that the conversion of the

imaginary magnetic induction field BI into the gravitomagnetic field Bgp follows from the transformation equation of

the electromagnetic field, which is a Lorentz transformation. Lorentz transformations not only act on spacetime but

also on the internal spin states, resulting in their mixing.24 The same is supposed to be true for the mixing of Hermetry

forms in internal space H8 . Thus the resulting field is

Bgp vBeI ; (7)

which means that, if the BeI of the London equation is directed along the z-axis, the resulting Bgp is pointing in eˆr

direction, if cylindrical coordinates are used. It should be noted that AeI is the imaginary vector potential that belongs

to Eq. 5. Thus the resulting gravitomagnetic field is

B+

g p = aI

6me

wIeˆr: (8)

As mentioned above, the Lorentz equation also holds for the gravitophoton force (it should be noted that the Maxwell

equations and the Einstein-Maxwell equations are similar, and the fully nonlinear equations Einstein field equations are

only of interest in the direct neighborhood of black holes or for distances comparable to the diameter of the Universe)

that is, the gravity-like force is given by

F = m vBgp m v(vBeI ); (9)

which means that the resulting force is in the direction of the BeI field, which, in the Heim experiment is the axial

direction. The gravitophoton g+

g pacceleration then has the form

gThe charge of the imaginary electron eI and electron e are the same.

V CONCLUSIONS AND FUTURE ACTIVITIES 14

g p = aI

6me

wI (10)

Since v is the circumferential speed of the rotating disk, the average velocity of the particles in the disk is given by

A =

v2 (11)

and therefore the axial acceleration is

gp = aI

2me

wI : (12)

Since finally the gravitophoton acceleration field is converted into a graviton field, the ratio of the gravitational

coupling factors GN G¤1

gp = 67 is introduced. The new variables appearing in the following equation are specified in

the numerical example below.

gg =

Ggp

2me

rDAD

r0DA0D

A0C

wI (13)

It should be mentioned that the real super-current in the coil is limited according to Eq. 14

IL =

2pR

A0C

6me

wI (14)

where R is the radius of the coil. Only for a real current I < IL imaginary electrons can assume part of the wire cross

section of the coil.

As an example for a laboratory experiment to producing a sizable axial field a disk of d = 0:2m diameter together

with the following parameters is used:

1836

r0D

=0:19,

A0D

103

, where r0D and A0D are reference density

and reference area of the disk, and N = 50 is the number of turns of the coil. A value of AC=A0C = 5 is chosen, where

AC and A0C are the cross section and the so called reference cross section of the coil, respectively. The circumferential

speed of the disk is v = 50 m s¤1 and wI = 105s¤1. Inserting these values results in

gg = 67

228

1836

0:19

103

505

2500

310¤8 105

9:81

g = 3:610¤2g (15)

where g denotes the acceleration of the Earth. For the limit of the real current IL one finds

I < IL =

2pR

A0C

6me

wI 10 A: (16)

V. Conclusions and Future Activities

Since 2002 ideas of a geometric approach (termed Extended Heim Theory (EHT)) were published by the authors

with the aim to determine all possible physical interactions and to associate to each interaction its proper metric

tensor. This goal is achieved by complementing four-dimensional spacetime with an internal eight-dimensional space

H8 comprising a set of four subspaces. It turned out that this approach, which differs form the introduction of extra

spatial dimensions, predicts six fundamental physical interactions, namely three types of gravitational fields,

electromagnetism as well as the weak and strong interactions9, 15, 16 . In EHT gravitation can be both attractive and

repulsive. EHT also predicts the existence of virtual particles of imaginary mass, responsible for the conversion of

electromagnetic into gravitational fields. There should be also three different types of photons. Imaginary particles

might be accountable for the invisible dark matter, recognizable only through its gravitational interaction with ordinary

matter. Charged ordinary and imaginary matter can also interact electromagnetically, because of the three different

types of photons postulated in EHT: g which is the ordinary photon, gI responsible for the interaction between charged

imaginary particles, and gIR that conveys the interaction between charged imaginary and real particles. Concerning the

speed of gravitational interactions, EHT, has determined three widely different propagation speeds.

• The interaction of Newtonian gravity (force) is almost instantaneous, that is cg = 2:51010c,

V CONCLUSIONS AND FUTURE ACTIVITIES 15

• the propagation speed of gravitational waves (energy) and neutral gravitophotons is c (speed of light in vacuum),

• the quintessence interaction, i.e. the repulsive part of gravitation, (acceleration of the Universe propagates at a

very low speed cI with c2 = cgcI , and thus imaginary particles can form at very low velocities. The velocity cI

is also the propagation speed of imaginary particles in matter.

• To all three propagation speeds their proper Lorentz transformation is assigned.

Numerous experiments by Tajmar et al. at AIT Seibersdorf carried out since 2003, and first published in 2006, report

on the laboratory generation of extreme gravitomagnetic as well as gravity-like fields, and thus seem to corroborate

the theoretical findings of EHT. The gravitomagnetic effects measured are about 18 orders of magnitude larger than

predicted by the so called Lense-Thirring effect of GR. In other words, the rotating niobium ring utilized by Tajmar et

al., having a mass of some 400 grams, produces a frame dragging effect similar to the mass of a white dwarf9 . These

experiments were repeated by Graham et al.37 in 2007, and more recently by Tajmar et al.36 including a comparison

between the two experiments.

If the experiments of Tajmar and Graham are correct, a similar effect should have been observed in the NASAStanford

Gravity-Probe B experiment as calculated in9 . Indeed, a large gyro anomaly was observed in GP-B, but

attributed to an electrostatic patch effect. In how far there is room for the extreme gravitomagnetic effect, as predicted

by EHT therefore is an open question. EHT was used to analyze all of these experiments, and also (approximately)

predicted the magnitude of the gyro misalignment in the GP-B experiment resulting from the postulated extreme

gravitomagnetic spin-spin interaction. The in orbit observed gyro misalignment was attributed to the generation of

gravity-like fields acting between the cryogenic Nb coated gyros (cf. Tajmar experiments) in each of the two gyro pairs.

The two counter-rotating gyro pairs utilized in the GB-P experiment exhibited asymmetric misalignment, depending on

the direction of their rotation. Theoretical predictions by EHT and measured misalignment were compared with the in

orbit measurements and gave reasonably good agreement. Hence, it remains to be seen whether the electrostatic patch

effect, used in the post-flight analysis to predict gyro misalignment by the Stanford team, is capable to completely

accounting of both the magnitude and the type of anomaly observed. According to EHT, this anomaly should not

be totally explainable by classical effects, i.e. electrostatic forces etc. The result of GP-B is that the Lense-Thirring

(frame dragging) effect exists exactly as predicted by GR though the initially targeted accuracy of 1% could not not

be obtained. Therefore, there is no room using a modification of the Lense-Thirring effect to explaining the huge

observed gravitomagnetic fields. The calculations done in9 fall into the range of the observed gyro misalignment, but

it can only be surmised that there is room for the extreme gravitomagnetic effect by EHT.

In summary, the present situation is characterized by the fact that numerous gravitational experiments have been

performed over a period of four years, employing different measurement techniques, showing similar, but unexpected

and unexplainable results if the framework of GR is employed. Measurement techniques in all experiments are clearly

state of the art, in particular for the GP-B experiment.

In all experiments a phase transition seems to have occurred at low temperature (not necessarily at TC, the critical

temperature for superconducting), and possibly boson interaction took place that is, formation of virtual bosonic

imaginary particles from imaginary electrons eI . GR cannot be used to explain these phenomena, even if the full

nonlinear Einstein field equations were used. The Lageos satellites and the GP-B experiment have clearly demonstrated

that the inertial frame dragging effect, even from celestial bodies, is extremely small and within GR. These facts

provide evidence for entirely novel physics in the form of additional long range fundamental forces. In this regard,

GR seems to be incomplete and not QM, something Einstein would have been shocked to learn about.

At present, there are qualitative but also substantial quantitative uncertainties concerning the theory of gravitomagnetic

physics. The unusual, laboratory generated extreme gravitomagnetic and gravity-like fields point to a novel

mechanism and, as predicted by EHT, may be the result of two additional gravity-like fields in combination with

non-ordinary matter, i.e. imaginary matter. The experiment for generating an axial field, termed Heim experiment,

is surprisingly simple and would not require excessive magnetic fields or currents, except that liquid He is necessary

to achieve the postulated phase transition. The Heim experiment can therefore be performed with current technology

and, if successful, would allow to engineer gravity in a way similar to electromagnetism. Of great practical importance

would also be the aspect of energy conversion from the direct interaction between electromagnetism and gravitation,

or from employing gravity-like fields as plasma stabilizers in nuclear fusion, for instance, in simple configurations like

magnetic mirrors.

The gravity-like fields would also lead to entirely novel technologies in the area of transportation be it on the

ground and on water, or in the air. In addition, these fields might also be usable in energy generation leading to energy

research that might be highly relevant for the near future.

VI ACKNOWLEDGMENT 16

The theoretical work to be performed needs to focus on both the fundamental aspects of the symmetry groups as

well as on determining the technical and experimental details in order to experimentally realize the proposed axial

field. Naturally, many theoretical questions remain open concerning the six fundamental forces as well as in particular

the role and the interaction scenarios of the postulated imaginary matter.

Most important, spacetime is supposed to have an active role being part of the physical system that means,

propellantless propulsion would interact with the spacetime field exchanging energy and momentum. Such a space

propulsion system would in principle lead to a minuscule acceleration of the Universe, though in practice this acceleration

would hardly be noticeable, in the same way the momentum change of a rowing boat, impeded by its sculls to

the total momentum of the water of the ocean, would remain undetectable.

VI. Acknowledgment

This paper is dedicated to Dr. William Berry (ret.), head of Aerothermodynamics and Propulsion Division, ESAESTEC,

Noordwijk, The Netherlands on the occasion of his 75th birthday.

The assistance by M.Sc. O. Rybatzki, Faculty Karl-Scharfenberg, Univ. of Applied Sciences, Salzgitter Campus

in preparing the figures is gratefully acknowledged.

The authors are grateful to Prof. Dr. M. Tajmar, KAIST Seoul, Korea for providing measured data as well as for

numerous comments regarding comparisons between EHT and the gravitomagnetic experiments.

The authors are most grateful to Prof. P. Dr. Dr. A. Resch, director of the Institut für Grenzgebiete derWissenschaft

(IGW), Innsbruck, Austria for his support in writing this paper.

The second author is indebted to his colleague Prof. Thomas Waldeer, Ostfalia Univ., Suderburg for proofreading

the paper and suggesting improvements.

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AIAA2010-021-NFF-1-heim drive.pdf (671,1 kB)

Advanced Propulsion Systems from Artificial Gravitational Fields

02.05.2014 11:43

AIAA5595JCP2007DarkAbbreviated.pdf (5,5 MB)

Advanced Propulsion Systems from

Artificial Gravitational Fields

Walter Dröscher and Jochem Hauser 1

Institut für Grenzgebiete der Wissenschaft, 6010 Innsbruck, Austria

Abbreviated Version 2

Figure 1. The cover picture shows a combination of three pictures. The background picture, taken from [1] shows a view (artist’s

impression) of a real planet orbiting the solar-type star HD222882 about 137 ly away from earth. The second picture shows all

messenger particles as predicted from Extended Heim Theory. It should be noted that EHT predicts three gravitational interactions,

which are described by messenger particles termed gravions, namely gravitons (attractive, ordinary matter), gravitophotons (attractive

and repulsive, dark matter), and the quintessence particle (repulsive, dark energy). The third picture depicts the principle of

gravito-magnetic space propulsion as derived from EHT. For further explanations see Fig. 7 of this paper.

3 4 5

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 AIAA 2007-5595, Session NFF-1, 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 8-11 July 2007, Cincinnati, OH

4 ©Institut für Grenzgebiete der Wissenschaft Innsbruck, Austria 2007

5 The mathematical derivations in this paper rely on concepts explained in paper [8]. For lack of space these concepts are not presented here, see

www.hpcc-space.de for download.

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. These limitations can only be

overcome if novel physical laws can be found. During the last two decades, numerous experiments related to gravity shielding or

gravito-magnetic interaction were carried out, but eventually all proved to be incorrect. However, in March 2006, the European

Space Agency (ESA) announced credible experimental results, reporting on the generation of artificial gravitational fields

(also termed gravito-magnetic fields, GMF), in the laboratory. The GMF was generated by a rotating niobium superconductor

ring, subjected to angular acceleration. The GMF existed only during the acceleration phase of the ring, counteracting the

mechanical acceleration, thus obeying some kind of gravitational Lenz rule. These experiments were performed by M. Tajmar

and colleagues from ARC Seibersdorf, Austria and C. de Matos from ESA, and since then were repeated with increased

accuracy, leading to the same results. 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 weakly repulsive gravitational like interaction. The paper starts with an introduction into the physical

concepts of EHT. In the next step, EHT will be used to explain two enigmatic phenomena of physics that cannot be described

by current physical theories, namely the gravitational effect of dark matter and the generation of artificial gravitational fields.

First, though the existence of dark matter was already suggested in the 1930s by Caltech astronomer Zwicky, its gravitational

interaction is still a riddle. It will be shown that the gravitophoton concept can be utilized to calculate both the distribution

of ordinary matter, dark matter, and dark energy as well as the separate gravitational coupling strengths for these three types

of matter. Next, the recent experiments by Tajmar et al. (the artificial gravitational force, however, was observed only in the

circumferential direction in the plane of the superconducting ring) will be analyzed, and a quantitative comparison between

EHT predictions and experiment is given. Finally, it is shown, provided EHT is correct, how gravitophoton interaction can 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 propellant. As it turns out, experimental

requirements to lift a spacecraft from the surface of the earth can be satisfied by current technology. Based on the gravitomagnetic

propulsion concept, mission times to the international space station (LEO), the planned moon basis, to Mars, and

missions to the outer planets are calculated. It will be shown that this propulsion system is far superior to any existing propulsion

technology, while its technology is far simpler than chemical propulsion.

1 ARTIFICIAL GRAVITATIONAL FIELDS FOR SPACE PROPULSION

Spaceflight as we know it, is based on the century old rocket equation that is an embodiment of the conservation

of linear momentum. Current space transportation systems are based on this 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. Moreover, special relativity

puts an upper limit on the speed of any space-vehicle in the form of the velocity of light in vacuum. The only possibility

to overcome these severe limitations lies in the finding of novel physical laws that allow constructing propulsion

systems based on principles different from classical mechanics (momentum principle). Therefore, there has been a

great deal of interest during the last decade in so called breakthrough propulsion physics.

On the other hand, modern physics cannot explain most basic questions, such as the nature of matter, the mass

spectrum of elementary particles or their corresponding lifetimes. In particular, the question concerning the number of

fundamental interactions cannot be answered by current theory, neither string theory nor quantum gravity. In one of his

latest papers, Einstein 1950 in Scientific American [2], stressed the necessity that any successful quantum field theory

aiming to unify fundamental physical forces, needs to be derived from the geometry of a dynamic spacetime. The late

German physicist B. Heim followed this idea and suggested a way to geometrize physics, but utilizing a quantized

spacetime [3]. At the same time a similar approach was suggested by the Italian mathematician B. Finzi [4].

Furthermore, since the 1930s observations of the large-scale motion of star systems within galaxies have suggested

the existence of non-baryonic matter (neither protons nor neutrons) that does not interact electromagnetically, and

therefore was termed dark matter because of its invisibility. The amount of dark matter is considerable, about 26 %,

while ordinary (baryonic) matter comprises some 4 to 5 % of all the matter in the universe. The major part of the

matter in the universe is dubbed dark energy and amounts to approximately 70 % [5]. Although the MOND (Modified

Newtonian Dynamics) hypothesis [6], which assumes a modified Newtonian law, can explain the rotation of stars

in most types of galaxies, it does not work for the inner parts of rich galaxy clusters. Moreover, in a recent article

in Nature [7], it has been shown that dark matter is real and reveals its existence through gravitational lensing that

cannot be explained by the MOND hypothesis. However, the MOND parameter, see below, can be used as a working

hypothesis, but not as the physical explanation of the phenomenon of dark matter.

Building on Heim’s idea of a poly-metric, in a series of papers, the authors proposed a unifying approach for all

physical interactions, [8], [9], termed Extended Heim Theory (EHT). As a consequence of its geometrical approach,

EHT predicts the existence of six fundamental forces, instead of the four known ones (gravitation, electromagnetism,

weak (radioactive decay), and strong interaction (atomic nuclei and elementary particles)). The two additional interactions

predicted in EHT are identified as gravitophoton interaction, enabling the conversion of photons into a

gravitational like field, represented by the two hypothetical gravitophoton (attractive and repulsive) particles (dark

matter), and quintessence, a weakly repulsive gravitational like interaction (dark energy). The interpretation of the

physical equations for the gravitophoton field leads to the conclusion that this field could be used to accelerate a

material body without the use of propellant. Therefore, gravitation, as we know it, seems to be comprised of three

interactions, the graviton (attractive), gravitophoton (attractive and repulsive), and the quintessence or vacuum

(repulsive) particle that is, there exist three quanta of gravitation. This means that the gravitational constant G

contains contributions of all three gravitational constants, termed GN;Ggp and Gq, respectively. The quintessence

interaction, however, is much smaller than the first two contributions. For further details see [10].

In the 1990s a Russian physicist claimed to have measured gravitational shielding. A similar claim was made by an

American scientist several years later. However, in their recent paper Woods et al. [11] have delivered overwhelming

experimental evidence that these two claims cannot be substantiated. This kind of gravitational shielding simply does

not exist.

In 2006, however, the experimental situation changed completely when M. Tajmar and his colleagues from

ARC Seibersdorf, Austria and de Matos from ESA [12, 13, 14, 15] published a series of papers reporting on the

measurement of artificial gravitational fields (AGF), generated by a rotating superconducting niobium ring. These

experiments were conducted over a period of four years, and utmost care was used by the experimenters to exclude

any noise effects. Moreover, in a recent oral communication M. Tajmar (May 2007) confirmed that his experimental

results (laser-gyro measurements) have been verified by another experimental group and are about to be published.

Everytime the superconducting niobium ring was subjected to angular acceleration, an AGF was measured in the

plane of the ring in circumferential direction. The induced acceleration field was opposite to the angular acceleration,

following some kind of gravitational Lenz rule. In addition, an acceleration field was also observed when the niobium

ring was rotating with constant angular velocity undergoing a phase change that is, from the normal to the superconducting

state. This was achieved by reducing the temperature below 7.2 K, the critical temperature for niobium. No

acceleration effects were seen with high-temperature superconductors. No acceleration was measured (averaged) when

the niobium ring was in the normal conducting state (Fig. 5). In October 2006 Tajmar et al. repeated their experiments

employing both accelerometers as well as laser ring-gyros that very accurately measured the gravito-magnetic field.

The AGF was clearly observed, and its rotational nature was determined by a set of four staggered accelerometers.

According to Tajmar et al. these experiments demonstrate that an AGF was generated by the magnetic field of the

rotating superconducting niobium ring, termed the gravito-magnetic London effect. Although these experiments need

to be validated independently, they present definitive indications that an interaction between electromagnetism and

gravitation should exist.

The ratio of the measured acceleration field and the angular acceleration of the rotating niobium ring, denoted as

coupling factor by Tajmar, is proportional to the theoretically predicted density of Cooper pairs. In addition, when

analyzing Tajmar’s experiments using EHT, it became clear that an experiment could be devised, demonstrating

the generation of an AGF in the vertical direction (along the axis of rotation), capable of lifting a body from the

surface of the earth. Due to this Boson coupling (Cooper pairs, Bose-Einstein Condensate) technical requirements like

magnetic induction strength, current density, supply power should easily be met. According to EHT, required values

are substantially lower than for the previously proposed experiment [10, 16, 17] that assumed Fermion coupling.

2 PHYSICAL CONCEPTS OF EXTENDED HEIM THEORY

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 [18]. 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.

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

[19], 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

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.

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.

In order to construct a physically meaningful metric sub-tensor (also called Hermetry form), it is postulated that

coordinates of internal spaces S2 (organization coordinates) or I2 (information coordinates) 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, for details see Tables 2, 4 of ref. [8]7.

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

6 There is of course a second aspect, namely the quantization of the spacetime field.

7 Tables 1-4 of ref. [8] were omitted from this paper because of lack of space

and photon Hermetry forms are described by different coordinates, they lead to different Christoffel symbols, and thus

to different geodesic equations. 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. 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. [8, 10, 16].

Because of the double coordinate transformation (see [8, 16, 17]) each component of any metric tensor describing

a Hermetry form is written as a partial sum whose elements are selected from the 64 components that comprise the

complete metric tensor, which results from the incorporation of internal symmetry space H8 . The formation of metric

tensors for Hermetry forms follows selection rules described in the publications cited above. Thus, a poly-metric

representing the six fundamental interactions (messenger particles) and particle classes is constructed. If space H8 is

omitted, EHT is reduced to GR, and only gravitation remains. It is obvious that a double coordinate transformation

does not change, for instance, the curvature of a surface, since it is an invariant. However, this fact is not relevant in

the construction process of the poly-metric. The physical reason for the double transformation is to provide spacetime

with additional degrees of freedom, which do exist. For instance, it is an empirical fact that particle pair production

can occur from the so called vacuum of spacetime. Only metric tensors representing Hermetry forms have physical

relevance, and it is clear from their contruction principle that all these tensors derived from the underlying poly-metric

are different. Consequently, their respective Gaussian curvatures, Kl , where l denotes the index of the corresponding

Hermetry form, must also be different. This is straightforward to observe, since Gaussian curvature is only a function

of the first fundamental form (metric tensor components) as well as their first and second derivatives, but does not

depend on the second fundamental form. Therefore, each Hermetry form Hl has its proper Gaussian curvature Kl , and

thus curves space according to its own specific metric. Following the rules of GR that interprets curvature of space as

gravitational interactions, Hermetry forms can be interpreted as physical interactions, see Tables [1-4] in [8]. Having

established the relationship between Hermetry forms and curvature of space, some remarks between the connection

of geometry and physics are in place. All internal coordinates of space H8 have dimension of length and via the

Compton wave length are connected to mass. In [8] it was proved that spacetime also must be quantized on the Planck

length scale. Moreover, it is well known that in the case of gravitation for the Newtonian limit, metric element g44 is

proportional to the gravitational potential equation. In this respect elements of any metric tensor are identified with

physical potentials.

In EHT ten different charges can be identified that is, 3 color charges for the strong force, 1 electric charge for

electromagnetic interaction, 2 charges for the weak force, 1 gravitational charge for ordinary matter (4.36 %) and

1 for dark energy (69 %) as well as 2 charges for dark matter, namely for both positive (repulsive, 2.66%) and

negative (attractive, 24 %) dark matter. The distribution of these four types of matter was calculated from EHT.

The general coupling constants for charges are given by w2n

= q2n

¯hc ;n = 1; :::; 10. The values of all coupling constants

were calculated from EHT and gravitational coupling constants were given in [8, 10]. In addition, the probability

amplitudes for conversion of photons into gravitophotons, wph_gp, and from gravitophoton into quintessence particles,

wgp_q, were also calculated. Approximate values of the coupling constants can be found in [20]. With the knowledge

of the coupling constants, the respective charges can be determined. Using the relation between metric elements and

potentials, a connection between geometry and physics for each physical interaction can be installed. So far, however,

a detailed analysis for each individual Hermetry form has to be carried out. The last idea that will be introduced is

the incorporation of charges into EHT. To this end, the approach taken was to replace real valued internal coordinates

xa by four-spinors. The usage of quaternions is also being investigated. This work is in progress and no conclusive

answers can be given at present.

2.1 Gravito-Magnetic Force by Photon Conversion into Gravitophotons

The force produced by gravitophoton generation is termed gravito-magnetic force. It is a gravitational force, but

it is caused by photons that are converted into neutral 8 gravitophotons, which eventually decay via two different

8 a gravitophoton is termed neutral if it does not interact with matter

channels. Regarding the Hermetry forms for the photon, H7, and the gravitophoton, H5, see Table 2 in [8], 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 gravitophoton is generated. The fundamental question is, of course, how

this mathematical process can be realized as 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 in two ways. In one case, a graviton and a quintessence particle can be generated, which is the case in the

experiment by Tajmar, termed GME I, see Sec. 4.2. In the second case, experiment GME II, see Sec. 4.3, a positive

(repulsive) and a negative (attractive) gravitophoton can be produced.

The process of conversion of photons into gravitophotons should be possible in two ways, namely via Fermion

(vacuum polarization) [10] and through Boson coupling (Bose-Einstein condensates). Boson coupling is described by

Eqs. (2), (3). These equations are termed conversion equations. The three conversion amplitudes have the following

meaning: the first equation in Eq. (3) is obtained from EHT [10], the probability amplitude wph_gp predicts the

conversion of photons into gravitophoton particles and was published already in 1996 [20]. The third probability

amplitude wgp for the photon coupling is given by the well known relation

ph =

4pe0

¯hc

: (1)

The production of gravitophoton particles through the polarization of the vacuum by conversion of photons into

gravitophotons, 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 [8], [16], and [17].With the advent

of Tajmar’s experiments this process is no longer of interest, since it needs very high magnetic induction fields of

about 25 Tesla for a technically relevant application (1g acceleration).

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.(2) and (3). 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. (2), 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 [20], see Eq. (11)

p. 64, Eq. (15) p. 74, and Eq. (16) p. 77.

wph¤wph_gp = iNwgp (2)

wph¤wph_gp = i

(1¤k)(1¤ka) ¤1

wph (3)

where i denotes the imaginary unit. Inserting Eq. (3) in to Eq. (2 results in the net production of gravitophotons. It

should be noted that the imaginary unit is needed, since the square of probability amplitudes also reflect charges.

Otherwise Eq. (3) may result in an increased electron charge. However, in the case of Boson coupling there are no

virtual charges that can lead to charge increase. Therefore probability amplitude wph_gp is of the form

Âwph_gp+iÁwph_gp = wphi

(1¤k)(1¤ka) ¤1

wph (4)

where the imaginary part is different from 0 in case of sufficient Cooper pair density.

2.2 Physical Mechanism for Gravito-Magnetic Force in GME I, II

In the following, a model for the physical mechanism of the conversion of photons into gravitophotons is presented,

providing a mathematical expression for the gravito-magnetic force. The mathematical steps are omitted, but final

quantitative results are given. It should be understood that such a model needs to be confirmed by experiment. The

model is based on plausible physical assumptions, derived from the fundamental principles of EHT, but no proof of

correctness in a mathematical sense is possible.

In Fermion coupling the additional charge is produced by the vacuum of spacetime, while in Boson coupling

the additional charge comes from the imaginary part of the Cooper pair charge. The Boson coupling therefore is a

condensed matter phenomenon. This means that for Boson coupling the probability amplitude (charge) wph remains

unchanged, in contrast to Fermion coupling. Instead, as can be seen from Eq. (3), it is the probability amplitude wph_gp

that is modified when the superconducting state is reached. Next, when Cooper pairs are set into motion, for example,

a ring rotating with constant angular frequency, the imaginary part of the charge e of the Cooper pairs gives rises to an

imaginary vector potential A that couples to the imaginary part of the proton charge of the ions in the crystal lattice.

The interaction of the two imaginary charge parts, however, leads to a real interaction energy. This would amount to

an electromagnetic interaction that cannot exist inside a superconductor. Therefore, it is assumed that the coupling

energy of the potential A is converted into gravitational energy, denoted by its proper gravitophoton potential Agp.

The gravitational potential, Agp, termed gravitophoton potential arises at the location of the protons, caused by the

generation of neutral gravitophoton particles. The relation between the two vector potentials is given by

mpAgp = eA (5)

Now we consider the Einstein-Maxwell formulation of linearized gravity that possesses a remarkable similarity to

the mathematical form of the electromagnetic Maxwell equations. In analogy to electromagnetism there exists a

gravitational scalar and vector potential, denoted by Fg and Ag. Introducing the corresponding gravito-electric and

gravito-magnetic fields

e := ¤ÑFg and b := ÑAg (6)

the linearized version of Einstein’s equations of GR can be cast in mathematical form similar to the Maxwell equations

of electrodynamics. Using Eq. (5) the gravitophoton field, bgp for niobium is obtained

bgp =

(1¤k)(1¤ka) ¤1

2 2me

w = 2:60910¤6w (7)

where w is the angular velocity of the rotating ring and the London moment, Eq. (11), was used. That is, the lasergyrometer

should produce a signal for the ring rotating with constant angular frequency w. For Pb the theory delivers

a somewhat lower value. As we have seen, EHT predicts that the magnetic induction field B is equivalent to a

gravitophoton (gravitational) field bgp. In the experiment by Tajmar et al. , a neutral gravitophoton decays into a

graviton and a quintessence particle, according to the theory of Hermetry forms. An AGF, however, will only be

generated if the ring is subjected to angular acceleration, i.e., if ¶bgp=¶t is different from 0, see Fig (4).

3 DARK ENERGY, DARK MATTER AND EHT

Here we only provide a brief discussion, because of the lack of space and second, because it is necessary to compare

physical models derived from EHT with experimental facts to see whether the models can stand this test. In any

case, the geometrization principle on which EHT is based, requires the existence of a fifth and sixth interaction,

which are identified as dark matter and dark energy. Furthermore, the charges for these interactions were identified

as gravitophoton (positive and negative) and quintessence particles. Their Hermetry forms were already given in [10].

EHT requires that positive (repulsive) dark matter also exists, however, at a much smaller amount than attractive dark

matter.

With the Chandra X-ray pictures of gravitational lensing there is striking astronomical evidence that there is a huge

amount of dark matter, optically invisible, but active in galaxies, in that orbital velocities of stars and gas clouds as

a function of distance from their galactic center contradict Kepler’s third law. Orbital velocities should decrease with

distance according to Kepler’s third law. Measured Doppler shifts for carbon monoxide and hydrogen spectral lines

Figure 2. The picture taken (see Chandra website) by the Chandra X-ray observatory in August 2006, shows for the first time the

clear separation of gravitational lensing resulting from ordinary matter, which comprises the hot gas in the cluster (pink) and from

dark matter (blue). The gravitational lensing effect of dark matter is substantially stronger. This picture proves that dark matter is

real, and that the MOND hypothesis of a modified Newtonian gravitational law is physically not correct.

show, for example in galaxy NGC1097, that orbital velocities almost remain constant or vrot = const. According to

Newton’s law vrot =

GNM(r)=r is expected. For NGC3198 an almost constant rotation velocity of 150 km/s was

measured between distances of 10 to 30 kpc (parsec). The amount of dark matter needed to explain this behavior is

in excess of all baryonic matter generated in the so called primordial nucleosynthesis. There is the possibility that

the process of nucleosynthesis is described incorrectly by current theory, or that another type of (invisible) matter

exists, not predicted by the standard model of physics. An alternative is to give up on Kepler’s third law. This has been

proposed by the so called MOND (Modified Newtonian Dynamics) hypothesis that can explain the rotation curves in

galaxies, but fails to explain orbital velocities in the core of galaxy clusters where there exists hot gas. Regarding Fig.

2 it is clear that dark matter is real and the MOND as a physical explanation is not correct, but the MOND parameter

can be used for quantitative determination of orbital velocities. Some fraction of the invisible matter is baryonic, but

from the study of X-ray emission of hot gas, in, for instance the bullet cluster, which contains the bulk of the ordinary

matter in the cluster, gravitational lensing shows a clear separation resulting from ordinary matter (pink) and dark

matter (blue), see Fig. 2.

The current status thus can be summarized such that a new type of invisible matter (dark matter), dominating

ordinary matter exists in the universe, but current physical theory cannot explain its nature. In the following some

ideas will be presented that should provide some insight on the physics of dark matter and energy.

In EHT, dark matter and dark energy are generated from masses that are calculated from elemental lengths, derived

from elemental surfaces of a quantized spacetime (spacetime becomes two-dimensional at the Planck length) that was

already postulated by Heim [21, 3, 22, 23], [10], and more recently by Rovelli et al. [26] and Kiefer [27]. According

to Rovelli the spectrum of elemental surfaces is given by (Heim used the simpler model of harmonic oscillator to

quantize spacetime)

aj = g G¯h

c3 ( j( j+1))1=2; j = n=2;n = 1;2; ::: (8)

where g = 1 was used, which is known as the Immirzi parameter that cannot be derived from quantum gravity. In the

following, the correspondence between length and mass is utilized as well as the idea, postulated also by Heim, that

mass was generated in the universe when the elementary length scale became small enough (symmetry breaking, phase

transition). This means that the universe existed without matter for a long period [10, 28, 29]. In concert with the fact

that three different types of matter exist the three elemental lengths derived from the first three states of a quantized

spacetime are associated with dark matter, (ordinary) matter, and dark energy that is,

lDM =

G¯h

4 p

3=4; j = 1=2; lM =

G¯h

4 p

2; j = 1; lDE =

G¯h

4 p

15=4; j = 3=2 (9)

The associated masses are

mDM = mpl

4 p

4=3; mM = mpl

4 p

1=2; mDE = mpl

4 p

4=15 (10)

where mpl = (¯h=G)1=2 = 2:17610¤8kg is the well known Planck mass and mDM > mM > mDE. These three types of

matter are represented by Hermetry forms H5 (degenerated), H1 and H9, respectively [10].

These elemental masses, mDM;mM and mDE were unstable and decayed. As was stated in [28] mass was produced

during this process, and, since no density higher than the Planck density, namely mpl=l3

pl can exist, the universe was

forced to expand.

After 5 billion years, the time dependence of dark matter changes into a constant energy density , in the same way as

for dark energy. Comparing the ratio of dark matter to dark energy, one obtains directly the factor 0:349 which leads to

a value of about 24.4 % of dark matter, while dark energy comprises about 70 % of all matter in the universe. Ordinary

matter 9 therefore accounts for approximately 5.6 %.

4 EHT ANALYSIS OF GRAVITO-MAGNETIC EXPERIMENTS

In the following EHT is used to perform an analysis of two gravito-magnetic experiments. The first one, termed gravitomagnetic

experiment one, GME I, concerns the analysis of the recent experiments by Tajmar et al.. as described in

Sec. 4.2. The second gravito-magnetic experiment, termed GME II, follows from theoretical considerations, obtained

from EHT, and would lead to an AGF of completely different nature than GME I, namely an AGF acting parallel to

the axis of rotation of the ring (disk), see Fig. 7, where the disk rotates with constant angular frequency.

GME II could serve as a demonstrator for a field propulsion principle without propellant as well as the basis

for a novel gravitational engineering technology. In GME II the superconducting rotating ring, employed in 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 EHT, the physical mechanism is different from GME I in that the neutral

gravitophoton decays into a positive (repulsive) and negative (attractive) gravitophoton, which causes the AGF to

be directed along the axis of rotation of the disk. The coupling to Bosons is the prevailing mechanism in both

experiments, but in GME I the resulting gravitophoton decays into a graviton and a quintessence particle. For Boson

coupling 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 prior to 2006, see, for instance, refs. [17], [16], [10].

Fig. 4 depicts the experiment (GME I) of Tajmar et al., where a superconducting ring is subjected 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. 7 describes the

experimental setup for GME II, the field propulsion device. Here 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. (GME I) need to accelerate the rotating

superconducting ring, producing the AGF in azimuthal direction. GME II uses a uniformly rotating disk, generating

an AGF directed along the axis of rotation. It is the latter experiment that could serve as the basis for a novel

propulsion technology - if EHT is correct. It will be shown in the following section that the postulated gravitophoton

force completely explains the experimental facts of GME I, both qualitatively and quantitatively. It is well known

experimentally that a rotating superconductor generates a magnetic induction field, the so called London moment.

9 A more detailed discussion on the topic of dark matter and dark energy is foreseen in a forthcoming review paper, due summer 2008

Figure 3. Theory explains superconductivity by the coupling of two electrons forming a so called Cooper pair. While a single

electron is a Fermion, a Cooper pair is a Boson. Without the presence of Cooper pairs, wph_gp = wph is a real value. According

to EHT, the motion of the Cooper pairs changes the value of probability amplitude wph_gp adding the imaginary part

(1¤k)(1¤ka) ¤1

wph so that the left-hand-side of Eq. (3) is obtained. Therefore, the probability (square of the amplitude) for

the conversion of photons into gravitophotons is different from 0.

4.1 Momentum and Energy Conservation for Gravito-Magnetic Force

In the following it will be shown that the neutral gravitophoton that causes the gravito-magnetic force can decay

via graviton and quintessence particle (GME I) or via positive (repulsive) gravitophoton and negative (attractive)

gravitophoton (GME II). In GME I, the AGF is in the circumferential direction and needs a time varying neutral

gravitophoton field, see Eq (12). In GME II the time varying differential operator is replaced by a spatially varying

operator, which should leading to a completely different nature of the gravito-magnetic force that is much more

amenable to space propulsion purposes.

In both cases the energy extracted from the vacuum is 0, since graviton and quintessence particles have negative and

positive energy densities, respectively. If in GME I, only the energy of the gravitons is measured, it should seem that

energy conservation is violated. However, this would be a clear sign that the energy budget is not complete, because

the positive energy density of the quintessence particle was not accounted for. In GME II, the total energy taken from

the vacuum is also 0. The two gravitophoton fields have opposite energy densities and add up to zero energy density.

As is shown in Eq. (16), the gravito-magnetic force from positive gravitophotons is directed along the axis of rotation,

while the gravito-magnetic force of the negative gravito-photons is in radial direction and exerts a force on the the

mechanical structure of the space vehicle.

Regarding momentum conservation this is, obviously, not conserved. Regardless whether a gravitational field is

generated by the mass of a planet or in the laboratory, it exerts the same force on a material body. Since the beginning

of space-flight, the gravitational fields of the planets have been used to accelerate a spacecraft. Any gravitational field

modifies spacetime and the spacecraft simply follows a geodesic trajectory. In this sense, there is no medium needed

for gravito-magnetic propulsion. The only difference to the well known gravity-assist technique is that instead of using

gravitational fields of the planets, the spacecraft is moving by its proper gravitational field, generated by the conversion

of photons into gravitophotons.

4.2 Gravito-Magnetic Experiment I

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.

It will be shown in the following section that the postulated gravitophoton force completely explains the experimental

facts of GME I, both qualitatively and quantitatively. It is well known experimentally that a rotating superconductor

Figure 4. Rotating superconducting torus (Niobium) modified from Tajmar et al., see ref. [15]. 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. [15] for the so called curl configuration that comprises a set of four accelerometers. In an earlier publication, see Fig.

4a) in [14], 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.

generates a magnetic induction field, the so called London moment

B = ¤

2me

w (11)

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.

4.3 EHT Analysis for Gravito-Magnetic Experiment I

Here 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. In GME I the neutral

gravitophoton decays into a graviton and a quintessence particle.

Without further demonstration, the gravitophoton acceleration for the in-Ring accelerometer is presented. It is

assumed that the accelerometer is located at distance r from the origin of the coordinate system. From Eq. (11) 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

w˙ reˆq (12)

where it was assumed that the B field is homogeneous over the integration area.

Figure 5. Picture taken from Tajmar et al., see [15]. In part (a), the Nb ring is in superconducting state. In the beginning, the ring

is rotating with constant angular frequency, and thus no AGF is present. As soon as the ring is subjected to angular acceleration

(red curve), an AGF is produced, causing the accelerometers to generate an acceleration field in opposite direction (black curve).

The AGF points in circumferential direction and is located in the plane of the ring, opposite to the angular acceleration. Thus no

propulsion force can be generated. In part (b), the ring is in normal conducting state, and regardless of its state of mechanical

motion, no AGF is observed. This is a clear indication that the presence of Cooper pairs (Boson coupling) seems to be responsible

for the generation of AGFs.

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. [15] were used. The following values were utilized:

w˙ = 103rad=s2; r = 3:610¤2m;

= 1=1836

ggp = ¤(0:04894)210¤43:610¤21039:81¤1g (13)

resulting in the computed value for the circumferential acceleration field

ggp = ¤4:7910¤6g (14)

For a more accurate comparison, the coupling factor 10 kgp for the in-Ring accelerometer, as defined by Tajmar, is

calculated from the value of Eq. (14), 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 11 these measurements [14] need to be repeated.

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 only could be calculated

for two materials, namely Nb and Pb.

In [15] 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 (15)

Comparing this with the equation derived from EHT, Eq. (14), 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 by

Tajmar , see [15], is overpredicting the measured value by about a factor of 2.

10 This coupling factor, as defined by Tajmar [15], is the ratio of the magnitudes of observed tangential acceleration ggp and applied angular

acceleration w˙ .

11 e-mail communication February 2007

Figure 6. Comparison of experiments GME I (Tajmar) and GMEII (gravito-magnetic propulsion experiment). GME II, derived

from EHT, is fundamentally different from GME I 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 itself is different. Second, the artificial

gravitational field generated would be directed along the axis of rotation. Hence, this acceleration field could 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.

Figure 7. In a gravito-magnetic propulsion device the payload would be above the rotating disk, since the acceleration field would

be generated above the disk. The propulsion would be very similar to gravity-assist technology, except that the planet producing the

gravitational field accelerating the spacecraft is being replaced by the AGF generated by the gravito-magnetic effect resulting from

the conversion of photons into gravitophotons. The vaccum itself would resume the role of the planet. In both cases, momentum of

the spacecraft is not conserved.

4.4 EHT and Gravito-Magnetic Experiment II

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

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. (7).

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

bz(ˆeq ˆez)ˆeq (16)

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. (7). In contrast to Fermion coupling, ref. [10], experimental

requirements are substantially lower.

According to our current understanding, the superconducting solenoid of special material (red), see Fig. (7), 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. (7)

describes the experimental setup utilizing a disk rotating directly above a superconducting solenoid. In the field

propulsion experiment of Fig. (7), the gravitophoton force produces a gravitational force above the disk in the zdirection.

5 TECHNICAL REQUIREMENTS AND PERFORMANCE OF GRAVITO-MAGNETIC

SPACE PROPULSION

Only a brief account is presented. The following assumptions were made for demonstration experiment GME II:

N = 10, number of turns of the solenoid, current of about 1A (needed to calculate bz), diameter of solenoid 0:18 m,

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 technological limits.

For a more realistic propulsion device in order to generate a force of 8:71105N, a mass of 3:15103kg and a

rotation speed of 200 m=s, a coil of 0:5 m diameter with 1,000 turns and a current of 1 A was calculated. The surface

area of the coils was determined to about 4 m2. These numbers will be recomputed in our forthcoming review article.

All trip times given in [10] remain unchanged, but as can be seen from the specifications above, technical requirements

were substantially reduced and should be feasible employing current technology. The reason for this change is Boson

instead of Fermion coupling.

CONCLUSIONS AND FUTURE ACTIVITIES

Since 2002 ideas for a fundamental physical theory, termed Extended Heim Theory (EHT), predicting two additional

gravitational interactions that might give rise to the generation of artificial gravitational fields (AGF), have been

published, see for instance, [8], [17], [16], [10]. A popular description of this research may be found in [32], [33],

[34].

EHT was used to describe the gravitational action of dark matter and dark energy, calculating the distribution

of the three (four) types of matter, namely ordinary matter, dark matter (attractive and repulsive), and dark energy

(repulsive) in the universe as well as the gravitational coupling of dark matter to ordinary matter. Second, EHT was

used to analyze the recent experiments by Tajmar et al. on the generation of AGFs (Sec. 4.2). This would be the

first experiment to generate an artificial gravitational field (AGF) and could lead to a new era of gravitational

engineering. A popular description of this research may be found in [30, 31]. The underlying physical mechanism

of the experiments as well as the direction and magnitude of the artificial acceleration field were calculated. Both

phenomena were explained using the concept of three gravitational interactions that is, the existence of six fundamental

forces as predicted by EHT. It should be noted that neither the behavior of dark matter can be explained by nor do

AGFs exist in current physical theories. The experimental results by Tajmar cannot be derived from the well known

frame dragging effect of GR, since measured values are more than 30 orders of magnitude larger than predicted by

GR, and thus should not be visible in the laboratory.

Furthermore, guidelines were established using EHT to devise a novel experiment for a field propulsion device

working without propellant, termed GME II (Sec. 4.3). In this experiment an AGF should be generated along the axis

of the rotating disk (ring) rotating with constant angular frequency. Initial calculations show that experimental

requirements are well within current technology. Boson coupling (Cooper pair density) seems to substantially alleviate

experimental requirements like magnetic field and current density. Future research should focus on the theoretical

aspects and experimental requirements of this device, because of its potential applications in the field of transportation.

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 for the two additional gravitational interactions were obtained from number theory, and

thus are calculated theoretically. It is interesting to note that they were already published in 1996 and used without

modification to explain and quantitatively compare with the experiments by Tajmar et al.

A gravito-magnetic propulsion device 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.

As a next step, experiment GME II should be analyzed in detail. Dark matter and dark energy predictions from EHT

should be investigated further. From the experimental side, major efforts should be devoted to validate or to falsify

the experiments by Tajmar et al. and to improve experimental accuracy. Tajmar’s experiments could well become

landmark experiments for the completely novel technology of gravitational engineering.

ACKNOWLEDGMENT

The assistance by MSc. O. Rybatzki, Faculty Karl-Scharfenberg, Univ. Applies Sciences, Salzgitter campus in preparing

the figures is gratefully acknowledged.

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 author gratefully acknowledges his

hospitality and the 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.

REFERENCES

1. Villard, R., L.R. Cook .: Infinite Worlds, University of California Press.

2. Einstein, A.: On the Generalized Theory of Gravitation, Scientific American, April 1950, Vol 182, NO.4.

3. Heim, B.: Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen, Zeitschrift für Naturforschung,

32a, 1977, pp. 233-243.

4. Cardone, F. and R. Mignani: Energy and Geometry, World Scientific, 2004.

5. Cline, D.B..: Does Dark Matter Really Exist, Scientific American, March 2003, pp. 42-52.

6. Cline, D.B. .: The Search for Dark Matter, Scientific American, August 2002, pp. 29-35.

7. Carroll, S..: Dark Matter is Real, nature physics VOL 2, October 2006, pp. 653-654.

8. Dröscher,W., J. Hauser: Spacetime Physics and Advanced Propulsion Concepts, AIAA 2006-4608, 42nd

AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Sacramento, CA, 9-12 July, 2006, 20 pp., (available

as revised extended version 20 August 2006 at www.hpcc-space.de).

9. Dröscher,W., J. Hauser: Current Research in Gravito-Magnetic Space Propulsion, Paper O-42, 7th International Symposium

on Launcher Technologies, 2-5 April 2007, Barcelona, Spain, 16 pp.

10. Dröscher,W., J. Hauser: Guidelines for a Space Propulsion Device Based on Heim’s Quantum Theory, AIAA 2004-3700,

40th AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Ft. Lauderdale, FL, 7-10 July, 2004, 21pp.

11. Woods C. et al.: Gravity Modification by High Temperature Superconductors, AIAA 2001-3363, 37 th AIAA/ASME

/SAE/ASE, Joint Propulsion Conference & Exhibit, Salt Lake City, Utah, 8-11 July, 2001.

12. de Matos, C. J., Tajmar, M.: Gravitomagnetic London Moment, and the Graviton Mass Inside a Superconductor, PHYSICA

C 432, 2005, pp.167-172.

13. M. Tajmar et al.: Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors, preprint

October 2006.

14. M. Tajmar et al.: Experimental Detection of the Gravitomagnetic London Moment, https://arxiv.org/abs/gr-qc/0603033, 2006.

15. M. Tajmar et al.: Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors, STAIF AIP,

February 2007. It should be noted that the values of the gyroscope output (bg field), plotted in Figs. (11, 12) of this reference,

have changed with regard to ref. [13]. We used the more recent values of the STAIF paper.

16. Dröscher,W., J. Hauser: Heim Quantum Theory for Space Propulsion Physics, AIP, STAIF, 2005, 10pp.

17. Dröscher,W., J. Hauser: Magnet Experiment to Measuring Space Propulsion Heim-Lorentz Force, AIAA 2005-4321, 41st

AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Tuscon, Arizona, 10-13 July, 2005, 10pp.

18. Veltmann, C.: Facts and Mysteries in Elelementary Particle Physics, World Scientific, 2003.

19. Zwiebach, R.: Introduction to String Theory, Cambridge Univ. Presss, 2004.

20. Heim. B., Dröscher, W.: Strukturen der Physikalischen Welt und ihrer nichtmateriellen Seite, Resch Verlagg, Innsbruck,

Austria, 1996.

21. Heim, B.: Das Prinzip der Dynamischen Kontrabarriere, Flugkörper, Heft 6-8, 1959.

22. Heim, B.: Elementarstrukturen der Materie, Band 1, 3. Auflage, Resch Verlag, Innsbruck, 1998.

23. Heim, B.: Elementarstrukturen der Materie, Band 2, 2. Auflage, Resch Verlag, Innsbruck, 1996.

24. : Cosmos, Scientific American, 2002, Vol 12, p. 36.

25. Schiller, C.: Motion Mountain, The Adventure of Physics, Chapter III, January 2007, www.motionmountain.net.

26. Rovelli, C.: Quantum Gravity, Cambridge University Press, 2004.

27. Kiefer, C.: Quantum Gravity, Oxford University Press, 2007.

28. Dröscher,W., J. Hauser: Future Space Propulsion Based on Heim’s Field Theory, AIAA 2003-4990, 39th

AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Huntsville, AL, 21-24 July, 2003, 25 pp.

29. Dröscher,W., J. Hauser: Physical Principles of Advanced Space Transportation Based on Heim’s Field Theory, AIAA

2002-2094, 39th AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Indianapolis, Indiana, 7-10 July, 2002,

21 pp.

30. T. Regitnig-Tillian: Antigravitation: Gibt es sie doch ?, P.M. 3/2007, pp. 38-43 and www.pm-magazin.de/audio.

31. S. Clark: Gravity’s Secret, 11/11 2006, New Scientist, pp.36-39, archive.newscienist.com.

32. H. Lietz: 11 Lichtjahre in 80 Tagen. Von der Feldtheorie Burkhard Heims und ihrer Anwendung für einen Raumfahrtantrieb,

Telepolis Special 1/2005, Heise Verlag: Hannover, S.47-51.

33. H. Lietz: Hyperdrive,7-13 January, 2006, New Scientist.,

34. H. Lietz: Plus Vite que la Lumière, Scilogic, 2006, pp. 89-94.

35. Czysz, P., Bruno, C.: Future Spacecraft Propulsion Systems, Springer 2006.

36. Kane, G.: Das Geheimnis der Materie, Spektrum der Wissenschaft, Februar 2007.

AIAA5595JCP2007DarkAbbreviated.pdf (5,5 MB)

Emerging Physics for Novel Field Propulsion Science

02.05.2014 11:24

AIP2010Hauser.pdf (1,2 MB)

Melville, New York, 2010

AIP CONFERENCE PROCEEDINGS 1208

EDITOR

Glen A. Robertson

Institute for Advanced Studies in the

Space, Propulsion & Energy Science

Madison, Alabama

SPONSORING ORGANIZATIONS

American Astronautical Society

American Institute of Aeronautics and Astronautics

Astrosociology Research Institute

All papers have been peer reviewed

14th Conference on Thermophysics Applications in Microgravity

7th Symposium on New Frontiers in Space Propulsion Sciences

2nd Symposium on Astrosociology

1st Symposium on High Frequency Gravitational Waves

Meeting on Future Directions in Space Science & Technology

Workshop on Future Energy Sources

Johns Hopkins - APL, Laurel, Maryland 23 - 25 February 2010

SPACE,PROPULSION &

ENERGY SCIENCES

INTERNATIONALFORUM

SPESIF-2010

Emerging Physics for Novel Field Propulsion Science

Jochem Hauser and Walter Dröscher

Faculty H, Ostfalia Univ. of Applied Sciences

Campus Suderburg, Germany

Institut fur Grenzgebiete der Wissenschaft

6010 Innsbruck, Austria

jh@hpcc-space.de

Abstract. All space vehicles in use today need some kind of fuel for operation. The basic physics underlying this

propulsion principle severely limits the specific impulse and/or available thrust. Launch capabilities from the surface of

the Earth require huge amounts of fuel. Hence, space flight, as envisaged by von Braun in the early 50s of the last

century, will not be possible using this concept. Only if novel physical principles are found can these limits be

overcome. Gravitational field propulsion is based on the generation of gravitational (gravity-like) fields by manmade

devices. In other words, gravity-like fields should be experimentally controllable. Present physics believes that there

are four fundamental interactions: strong (nuclei), weak (radioactive decay), electromagnetism and Newtonian

gravitation. As experience has shown for the last six decades, none of these physical interactions is suitable as a basis

for novel space propulsion. None of the advanced physical theories like string theory or quantum gravity, go beyond

these four known interactions. On the contrary, recent results from causal dynamical triangulation simulations indicate

that wormholes in spacetime do not seem to exist, and thus even this type of exotic space travel may well be

impossible. Recently, novel physical concepts were published that might lead to advanced space propulsion

technology, represented by two additional long range gravitational-like force fields that would be both attractive and

repulsive, resulting from interaction of gravity with electromagnetism. A propulsion technology, based on these novel

long range fields, would be working without propellant.

Keywords: Six Fundamental Physical Forces, Three Different Gravitational Fields, Ordinary And Non-Ordinary

Matter, Generation Of Gravity-Like Fields In The Laboratory, Interaction Between Electromagnetism And

Gravitation, Propellantless Propulsion, Extended Heim Theory (EHT).

PACS: 03., 11., 77., 04.80 Cc

INTRODUCTION

The 40th anniversary of the Moon landings has come and gone, but the future of humans going back to the Moon

looks grim, not even considering a Mars mission, which seems next to impossible. The problem is inadequate

propulsion. The current status of space propulsion is characterized by two contradicting scenarios. The first one,

chemical propulsion delivers high thrust but for several minutes only at relatively low specific impulse, and is used

today to lift heavy payloads from the surface of the Earth into nearby space (for instance LEO). The second one,

electric and plasmadynamic propulsion, provides low thrust over longer periods of time (up to several months) at

high specific impulse, and is employed in scientific interplanetary missions of long duration. Propulsion systems can

be classified according to their physical principles as thermal propulsion systems or electromagnetic propulsion

systems. Advanced versions of these systems are described in the recent book by Bruno and Accetura (2008), which

performs a linear extrapolation of present technology, envisaged of being realizable in 2020. Another class of

advanced concepts using photonic propulsion, solar sails, or laser propulsion has been suggested. Comparing these

advanced concepts with the space propulsion concepts discussed in the books by Seifert (1959) and Corliss (1960) it

becomes obvious that the physical principles of all of these concepts have been around for several decades, but

with regard to performance no significant progress has been achieved. Even the much discussed wormholes most

likely do not exist as was shown by Ambjorn (2008) and Loll (2008), and thus even this type of exotic space travel

may well be impossible.

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The reason for this lack in progress is that physical laws pose strict limits on the practicality and the performance of

even the most advanced propulsion systems, and in practice have prevented the construction of efficient and effective

propulsion systems. First, all systems considered so far operate on the basis of expulsion of mass and energy, i.e.,

have to obey classical momentum conservation. Hence, some kind of propellant needs to be provided. Second, the

speed of light in vacuum is limited by special relativity, so interstellar travel in general does not seem to be feasible

in our spacetime. This, however, is not at all a concern at present, since our current chemical propulsion systems are

delivering velocities of about 10 km/s.

The question naturally are there any, hitherto unknown, physical phenomena that might justify the existence of

additional physical interactions? The answer seems to be affirmative. In March 2006, the European Space Agency

(ESA), on their webpage, announced credible experimental results, reporting on the generation of both

gravitomagnetic (termed frame dragging in GR, which, however, is too small to be measured in a laboratory on

Earth) and gravity-like or gravitoelectric fields, which are acceleration fields, performed at AIT Seibersdorf,

Austria. In analogy to electromagnetism, gravity-like fields are denoted as gravitoelectric fields, EG , since they

actually produce an acceleration. One speaks of a gravitoelectric force if the EG field is generated by a stationary

mass. The term gravitomagnetic force is used if EG vBG , i.e. the field is produced by a rotating mass together

with a mass density current. The field BG is called gravitomagnetic field. Since then, numerous experimental

results have been published by Tajmar et al. (2006, 2007a and 2007b) and Graham et al. (2007) whom published a

paper on the generation of a gravitomagnetic field produced by a cryogenic lead disk, but using a completely

different measurement technique. However, their results are not conclusive, since the sensitivity of their ring laser

was about two orders of magnitude lower than the gyro employed at AIT, but they also clearly saw a change in sign

of the gravitomagnetic field when the direction of rotation changed. In addition, in 2008 Tajmar et al. (2008)

published a more comprehensive set of gravitomagnetic experiments. Furthermore, in 2007 results of the NASA

Stanford Gravity-Probe B (GP-B) experiment (Kahn, 2008) became available, and EHT was used to model the gyro

anomaly seen in this experiment as well as the acceleration and deceleration of the two gyro pairs (see Dröscher and

Hauser, 2008).

GR predicts that any rotating massive body (Earth) drags its local spacetime around, called the frame dragging

effect, generating the so-called gravitomagnetic field. This effect, predicted by Lense and Thirring in 1918,

however, is far too small to be seen in a laboratory on Earth. For this reason the Gravity-Probe B (GP-B) experiment

was launched in 2004. On the other hand, the values measured by Tajmar et al. (2007b and 2008) were about 18

orders of magnitude higher than predicted by GR, and therefore are outside GR. They cannot be explained by the

classical frame dragging effect of GR and would represent a new kind of physical phenomenon. In other words, the

superconducting Nb ring in the laboratory, with a mass of about 500 grams, caused approximately the same

gravitomagnetic effect as a white dwarf (Dröscher and Hauser, 2008). In this context, it is highly interesting to

compare this scenario with the so called dipole gravitational field generator, first conceived by Forward as recently

described by Davis in Chapter 4 of Millis and Davis (2009). Instead of an electric current, Forward used a mass flow

together with the Lense-Thirring effect, to produce a gravitomagnetic field BG . He showed that the mass of a white

dwarf needed to be rotated to obtain an appreciable effect, see Davis. From an engineering standpoint his concept is

totally unrealistic. However, compared to the recent experimental results of Tajmar, a Tajmar-Forward dipole

gravitational field generator would invalidate these conclusions. Therefore, if the experiments by Tajmar et al.

(2007b and 2008) are correct, their physical roots must be outside GR, and thus would support the prediction of EHT

about the existence of additional long range force fields. In these experiments there seems to be something that

increases the gravitational permeability of the vacuum, 16 Gg / c2 , by many orders of magnitude. The control

parameter is temperatureT and a phase transition seems to occur at a certain, material dependent, critical

temperature TC , not necessarily identical with the formation of Cooper pairs.

Since this novel effect only occurs at cryogenic temperatures, it is surmised that a phase change takes place. EHT

postulates that this phase change is leading to novel particles. These virtual particles are identified as imaginary

mass electron pairs (Boson coupling, Bose-Einstein Condensate), interacting similar like Cooper pairs in

superconductivity, but producing a final force that is gravity-like.

169

According to EHT, regarding the construction of an advanced propulsion device, a genuine base experiment might

be feasible, in which the gravitoelectric field is directed along the axis of rotation, and thus could provide the

required direct mechanism for a field propulsion principle working without propellant. In addition, it is argued that

the experiment can be scaled such that a propulsion system can be constructed to lift a sizable mass from the surface

of the Earth. Based on considerations of EHT, the technical requirements like magnetic induction field strength,

current density, and supply power are calculated. The numbers obtained should be met with present technology.

Naturally, such a propellantless propulsion system would be far superior over any existing propulsion technology,

while its technology might be substantially simpler and cleaner than chemical, fission, or fusion rockets. There is, of

course, insufficient knowledge at present, both theoretical and experimental, to guarantee the realization of such a

device. However, the benefits of such a device are formidable.

GRAVITY AND GRAVITATIONAL FIELDS

In EHT it is argued that spacetime is the stage for physical processes, but it is to be complemented by the internal

space H8 that gives rise to the physical interactions and particles, because of the so called double coordinate

transformation (see Dröscher and Hauser, 2006 and 2007b). If this picture is accepted, it turns out that, surprisingly,

it is classical physics that seems to be incomplete, needed to be complemented by two additional fundamental

force fields that are gravity-like. Consequently, the integration of classical physics and quantum mechanics appears

in a new framework, and in this context the unification of physics might be possible. Another consequence of

internal space H8 is the existence of non-ordinary matter, see Figure 4, which has implications on both momentum

as well as energy conservation.

For the subsequent discussion, a note on terminology seems to be in place. Any force field acting on a massive

particle (rest mass different from zero) is termed gravitational field. Newtonian gravitation is the classical attractive

force acting between two masses. Gravity-like fields are acceleration fields produced and controlled by an

apparatus and may be both attractive and repulsive. The gravitomagnetic field, dimension (1/s), is the gravitational

counterpart of the magnetic induction field. It can be generated by a large rotating mass (planet or star), Lense-

Thirring effect, which follows from the linearized Einstein equations. The novel alternative is to use the

experimental setup of Tajmar et al. (2007b and 2008) or Graham et al. (2007) and generate a gravitomagnetic field

that is about 18 orders of magnitude larger than predicted by GR.

In EHT the existence of two additional gravity-like fields is predicted, and therefore a set of three coupled

gravitational fields needs to be considered. Moreover, a conversion of photons into neutral gravitophotons gp

can take place, coupling electromagnetism with gravitation, which leads to the generation of the strong

gravitomagnetic fields of the Tajmar effect in comparison with GR. Hence, classical physics may, under special

experimental conditions, lead to hitherto unknown phase transitions, and thus exhibit completely novel physical

phenomena in the form of long range force fields.

If spacetime is made of discrete pieces that is, atoms of spacetime exist, e.g. (Smolin, 2004), then spacetime might

be susceptible to collective modes, representing a daunting many-body problem. A major rearrangement of the

many-atom spacetime ground state could take place in the new symmetry-broken phase. Each phase of spacetime,

similar to phenomena observed in condensed matter physics, may exhibit its proper fundamental symmetry,

characterizing this phase. Hence, spacetime would assume the role of physical field(s) (particles), and therefore

should be accounted for in all physical processes of conservation of energy and momentum. These remarks

should only serve as general qualitative explanation for the recently observed large gravitomagnetic effects.

According to EHT, in the experiments of Tajmar et al. (2007b and 2008), the angular acceleration of the cryogenic

Nb ring should lead to a gravitophoton (gravitomagnetic) force. The following predictions are made by EHT for the

measured gravitational fields that are attributed to the conversion of photons into gravitophotons.

For the actual experiment as done by Tajmar et al. (2007b and 2008), the gravitophoton force is in the

azimuthal (tangential) direction, caused by the angular acceleration of the superconducting Nb disk. The

170

acceleration field is acting opposite to the angular acceleration, obeying some kind of gravitational Lenz

rule.

For the novel experiment of Figure 5 (field propulsion experiment), derived from EHT, a force component

in the axial direction should be generated while the ring or disk is rotating at constant angular velocity.

Building Blocks of Physics

In order for physical events to manifest themselves in our four-dimensional spacetime three basic building blocks

have to be present. The first one is the existence of four-dimensional spacetime, termed also external spacetime that

acts as the stage on which all physical events occur. The second building block is an internal space, called Heim

space, denoted H8 , which is responsible for the existence of the physical actors, namely the physical interactions

and matter. Each of the interactions or material particles is described by its so called Hermetry form (hermeneutics

of geometry, i.e., the physical meaning of geometry). A Hermetry form is a special metric tensor resulting from the

double coordinate system transformation mandated by the existence of internal Heim space (Dröscher and Hauser,

2006 and 2007a). The third building block is the substructure or subgroup structure that each Hermetry form

possesses, since it metric comprises a set of partial terms. The subgroup describes, for instance, the number of

different particles in the group.

1. Spacetime possesses an additional internal structure, described by an internal symmetry space, Heim

space, H8 , which is attached to each point of the spacetime manifold,

2. Polymetric tensor from which to construct Hermetry forms (metric subtensor that has physical meaning),

3. Symmetry breaking: alternative interpretation to spontaneous symmetry breaking, namely, instead of

symmetry breaking, the existence of virtual particles of imaginary mass is postulated that, being generated

in a solid at cryogenic temperatures, are not tachyons, but lead to the interaction between electromagnetism

and gravitation,

4. The set of Hermetry forms predicts the existence of ordinary and non-ordinary matter, including a class of

stable neutral leptons as well as virtual particles of imaginary mass,

5. Re-interpretation of conservation principles of momentum and energy to be applied to the complete

physical system comprising both ordinary and non-ordinary matter.

Double Coordinate Transformation

In this section some of the details of constructing the polymetric tensor as used in EHT are presented. The polymeric

tensor gives rise to a set of 15 metric subtensors that possess a physical meaning. Such a subtensor is also termed a

Hermetry form. The concept of an internal 8D space, termed Heim space, which comprises four subspaces, leads to

a major modification of the general transformation from general relativity GR and is assumed to account for all

physical particles and their interactions.

In GR there are two sets of coordinates, Cartesian coordinates x and curvilinear coordinates linked by a relation

between their corresponding coordinate differentials. If Heim space did not exist, the polymetric of EHT collapsed

to the mono-metric of GR.

Single Metric Tensor of GR

In GR there only four-dimensional spacetime exists, i.e. there is no internal space, comprising the time coordinate

with negative signature (-) and three spatial coordinates with positive signature (+) that is, the Lorentzian metric of

has one time-like (- signature) and three spatial (+ signature) coordinates (numbering of coordinates is 0, 1, 2, 3).

Signatures are not unique and may be reversed. 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). 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 . Let coordinates x with 1,...,4 denote

171

Cartesian coordinates x1 x, x2 y, x3 z, x4 ct . A general coordinate system for a spacetime manifold,M,

needs to be described by curvilinear coordinates with 1,..., 4 and ( )

M. In GR the equations relating

the two systems of coordinates are given by x x ( ) or (x ) . In GR, the distance between two

neighboring events with coordinates and d is given by the square of the line element

ds2 g d d , , 1,...,4

where the metric tensor is of the form

g · x x

e e (1)

and

with x ˆ

x e . The vectors e are the curvilinear (covariant) base vectors and eˆ denote the

Cartesian unit vectors. Since there is only one metric tensor, GR describes one interaction only; associated with

Newtonian gravity, see Figure 1a. The question arises, if this concept were valid for all physical interactions, how to

construct a set of metric tensors or polymetric.

Polymetric Tensor and Double Coordinate Transformation

In this section, the set of metric subtensors is constructed from the concept of Heim space, H8 , each of them

describing a class of physical phenomena (physical interaction or particles). This leads to the concept of Hermetry

form, to be introduced later. Thus, the connection between physical space and physics (symmetries) is established in

a way foreseen by Einstein, namely by the geometrical properties of spacetime. However, in order to reach this

objective, spacetime had to be complemented by an internal space H8 to model its intrinsic physical properties.

Once the internal space with its set of coordinates has been determined, everything else is fixed, and equation (2) is

a direct consequence ofH8 . In contrast to GR, now the relation between the coordinate systems (xi ) and ( j ) is via

the internal space with coordinates a that is xi xi ( a ( j )) or j j ( a (xi )) where index a is running from 1

to 8. This approach is fundamentally different form GR, Figure 1a, since a set of 15 different 4 4 metric tensors

is constructed that all live in four-dimensional spacetime. The existence of internal space H8 demands a more

general coordinate transformation from a spacetime manifold. In the concrete case of GR spacetime manifold M4

would be used M to a manifold N via the mapping M(locally R4) H8 N (locally R4

). Therefore in EHT, a

double transformation, equation (2), involving Heim space occurs. The global metric tensor is of the form

a b

g x x

(2)

where indices a,b 1,., 8 and , , 1,., 4 , and thus g comprises 64 components, see Figure 1b.

The length, being geometric, is invariant under reparametrization, and thus equations (1) and (2) described exactly

the same geometric object. So it seems that nothing has been achieved by this double coordinate transformation,

since, naturally, all other geometrical features of the manifold remain also invariant.

However, the associated complete metric tensor, equation (2), with its total of 64 terms, equation (3), does not have

any physical meaning by itself. The construction process for the set of the Hermetry forms is accomplished as

follows.

Extracting a certain number of terms from the global metric described by equation (2) by employing the selection

rules to be stated later, the complete set of 15 different Hermetry forms is eventually obtained.

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(a) (b)

Figure 1. In GR the metric tensor is computed using a mapping from manifold Mto manifoldN. (a) This type of mapping gives

one metric tensor that was associated with Newtonian gravitation by Einstein. (b) In EHT, a double coordinate

transformation is used incorporating internal space H8 that leads to a polymetric tensor from which the individual

Hermetry forms are constructed.

A single component of the metric tensor belonging to one of the four subspaces is given by equation (3). Only

special combinations of the gik reflect physical quantities, i.e. Hermetry forms. 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, equation (2), are set to zero. Hence, each Hermetry form is marked by the fact that only a subset of the

64 components is present. This subset is different for each Hermetry form. Therefore each Hermetry form leads to a

different metric in the spacetime manifold, and thus describes a different physical phenomenon. In other words, this

approach is equivalent to the solidarity principle of Finzi (see: Cardone and Mignani, 2004), namely each class of

physical phenomena (Hermetry form) determines its proper curvature in four-dimensional spacetime. This is why

equation (2) is termed the polymetric tensor. It serves as a repository for the 15 Hermetry forms. This construction

principle is totally different from Einstein's approach. Only in the special case of vanishing space H8 , EHT reduces

to GR,

( ) ( )

( ) ( ) .

a b

g x x

(3)

The polymetric tensor can be written as

, 1

a b.

a b

g g

(4)

A single Hermetry form is given by

, ,

( ) : a b : ( , )

a b H a b H

g H g a b

. (5)

Any Hermetry form can be written as the sum of its symmetric and anti-symmetric part, where indices S and A

denote the splitting of the partial metric terms into their symmetric and anti-symmetric parts

( , ) : 1 [( , ) ( , )] , ( , ) : 1 [( , ) ( )].

S 2 A 2 a b a b b a a b a b b a (6)

For instance, the Hermetry form of the neutral gravitophoton field which, in the experiments by Tajmar et al. (2006,

2007a and 2007b), decays into a graviton and a quintessence particle, gp g q , see Figure 3, is represented as

H( g q ) H( g ) H( q ) (7)

where the Hermetry forms of the graviton and the quintessence particle can be written in the form

H( g ) (55)S (56)S (66)S , H( q ) (77)S (78)A (88)S . (8)

The metric tensor representing any Hermetry form can therefore be written in general form

173

( ) ( , )S A.

a b H

g H a b

(9)

Six Fundamental Physical Forces

The polymetric tensor constructed in EHT gives rise to six fundamental forces (interactions) that are depicted in

Figure 2. Since GR uses pure spacetime only, as a consequence, there is only one metric tensor and hence only part

of the physical world is visible in the form of Newtonian gravitation. In order to describe all physical forces, the

polymetric tensor resulting from Heim space needs to be employed, see for instance (Dröscher and Hauser, 2006).

Figure 2. Six fundamental forces are predicted by EHT. Three of them are gravity-like (acceleration) fields (upper row,

coupling strengths), mediated by three field quanta termed graviton (attractive), gravitophoton (attractive and

repulsive), and quintesssence particle (repulsive). The second row shows the electromagnetic, weak, and strong

interactions. Arrows indicate possible coupling between interactions. Corresponding Hermetry (metric tensors) forms

are listed in Tables 1 and 2.

This idea was first conceived by Heim (1977), a German physicist. A similar principle was mentioned by the Italian

mathematician Finzi (see: Cardone and Mignani, 2004). The polymetric tensor of EHT, resulting from the concept of

H8 internal symmetry space and its four subspaces, is subdivided into a set of metric sub-tensors. Each element of

this set, denoted as Hermetry form, is equivalent to a physical interaction (e.g. gluons, see Table 1) or class of

particles (e.g. charged leptons, see Table 1), and thus the geometrization of physics may be achieved. Of course,

the question remains how to construct the energy-momentum tensor from the metric tensor in order to close the

system of equations. There is of course a further aspect, namely the quantization of the associated metric fields that

should result in the respective mediator bosons.

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 (Veltmann, 2003). In EHT, considered as the

natural extension of GR, matter seems to be a consequence of the internal space H8 . 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 point-like elementary particle is highly useful as a working hypothesis in

particle physics.

174

Hermetry Forms: Ordinary and Non-Ordinary Matter

Naturally, the number and type of interactions depend on the structure of internal space H8 whose subspace

composition along with the physical meaning of the individual subspaces was discussed in (Dröscher and Hauser,

2008, 2007a, 2007b and 2006). Contrary to the ideas employed in string theory, see for example (Zwiebach, 2009),

H8 is an internal space of 8 dimensions comprising four subspaces denoted R3 , T1 , S2 and I2 .

The Nature of Internal Space H8

In mathematical terms, H8 is the direct sum of its four subspaces, i.e., H8=R3 T1 S2 I2 . This means that

dim H8 = dim R3 + dim T1 + dim S2 + dim I2 = 3 + 2 +2 +1.

Furthermore, the decomposition for any vector a

H8 is unique. With the introduction of the four subspaces of

H8 a symmetry breaking has been introduced ad hoc, which is causing the formation of physical entities as well as

physical structures via Hermetry forms, see below. Furthermore, this subspace structure of H8 leads to a group,

termed Heim group, H O(3, q)O(2, q)O(2, q)O(1, q) over the set of quaternions that is q

. Quaternions

possess the simplest non-commutative algebra. This is deemed to be necessary to reflect the fact that spacetime

ultimately is not a continuum, but instead is assumed to be a non-commutative Riemannian space. Quaternionic

probability amplitudes, according to Heim space H8 , are subject to gauge transformations which results in

15 6 6 1 28 generators, to which potentials or particles are assigned. The O(3, q) delivers 15 fundamental

groups of particles (here group is not a group in the mathematical sense) of gravitational or non-gravitational nature,

while the O(2, q)O(2, q) stands for the 6 Higgs and 6 anti-Higgs bosons, responsible for all types of charges that

fundamental particles can possess. It is believed that all particles of OM or NOM, see Tables 1 and 2, interact with

its respective Higgs particle and gain charge (e.g mass or electric charge etc.), but their inertia (energy) should come

from groupO(1, q) , which denotes a special Hermetry form, H16 from subspace T1 , related to energy (mass)

via E t .

With regard to Heim space H8 , in physical terms, the R3 subspace coordinates are responsible for the existence

of mass, S2 for the formation of organizational structures (neg-entropy), I2 for information structures

(entropy), and the T1 subspace coordinate for the existence of charges.

The introduced symmetry breaking is necessary to account for the observational facts, namely that the Universe,

during its evolution, has produced massive particles as well as charges.

To each Hermetry form (metric subtensor), whose metric tensor is composed from the coordinates of the four

subspaces, its proper symmetry group is associated, leading to a hierarchical group structure. That is, there seems to

be no single monster group comprising all conceivable physics. In turn, each Hermetry form comprises its own

specific set of partial metric terms. So far the correspondence between these terms and their symmetry group has not

been worked out.

For instance, the graviton g Hermetry form H1 , is described by the group of spacetime symmetries (Lorentz and

Poincare) SO(3,1) and P(3,1) . The photon, , denoted by H2 , has symmetry U(1) etc., for the complete

representation see Table 1.

However, there is also the table of non-ordinary matter whose Hermetry forms lead to novel groups, such as for the

neutral gravito-photon, gp denoted by Hermetry form H9 and represented by symmetry group SO(4) , see Table2.

Hence, H8 allows the construction of a polymetric, while in string theory only a higher-dimensional mono-metric

exists. Although this mono-metric tensor can be further subdivided (broken symmetry) in order to give the four

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known physical forces, its ad-hoc construction does not provide the stringent fundamental physical insights from

which the complete set of physical interactions can be derived.

The crucial point for the polymetric tensor lies in the construction as well as the substructure (responsible for the

number of Hermetry forms) of the internal spaceH8 . The subspace composition should be derived from basic

physical assumptions, which must be generally acceptable. In other words, as GR does not employ any internal

space, it thus has limited geometrical structure, namely that of pure spacetime only. Because of this limitation, GR

cannot describe other physical interactions than Newtonian gravity, and consequently needs to be extended to reflect

a more comprehensive physical reality. EHT in its present form without any quantization, i.e., not using a discrete

spacetime, reduces to GR when the 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 is equating the Einstein curvature tensor, constructed from the metric tensor, to

the energy-stress tensor, representing energy-momentum distribution. In this way, the metric tensor field has become

a physical object whose behavior is governed by an action principle, like that of other physical fields. H8 is an

internal gauge space of 8 dimensions, responsible for physical interactions in our spacetime. As it turns out this

space admits 15 different Hermetry forms H with 1,.,15 . It is mentioned that six Higgs fields for ordinary

matter and six anti-Higgs fields for non-ordinary matter (see Tables 1 and 2) should exist, see next section. In

quantum field theory, once the Lagrangian is known, the rate of a physical process can be calculated. This is very

general, because it is not known why certain Lagrangians describe Nature and how many are needed. In EHT, it is

claimed that from the set of 16 Hermetry forms all physically possible Lagrangians can be determined. In this way,

Hermetry forms are the standard building blocks of physics, and from knowing their number and meaning, it is

concluded that six fundamental interactions exist.

Ordinary and Non-Ordinary Matter

The two matter tables depict the classification scheme for physical interactions and particles as obtained from the

polymetric of space H8 or Heim space. Superscripts for subspaces indicate dimension. A Hermetry form

characterizes either a physical interaction or class of particles, and is represented by the metric of an admissible

subspace (a space thus has real physical meaning) of H8 , which is a combination of the four elementary subspaces

as mentioned above. Any admissible subspace combination needs S2 or I2 coordinates to be present in order to

realize physical events in our spacetime. Employing this selection rule leads to 12 admissible Hermetry forms, plus

three so called degenerated Hermetry forms, and together with the special Hermetry form of the inertia field (see

below) there exists a total of 16 Hermetry forms. The four different colors in the messenger particle column indicate

the four known fundamental interactions. Any Hermetry form containing subspace R3 is associated with ordinary

(real matter), see Tables 1 and 2. Although gluons are supposed to have zero mass, the mass of the proton, about 1

GeV, is much larger than the sum of the masses of its three quarks, uud, which amount to some 10 MeV. Within the

proton radius the interaction energy between the three quarks, as permeated by the gluons, i.e. their color fields,

contributes the missing mass. Therefore, it is reasonable to assume that subspace R3 occurs in the Hermetry form

for gluons H5 . Moreover, the presence of R3 in the neutrino Hermetry form H7 requires that neutrinos have real

mass. Furthermore, the combination of subspaces R3 and T1 indicates charged particles of real mass. The

correspondences between Hermetry forms of Tables 1 and 2 should be noted, in particular the correspondence

between neutrinos and dark matter.

The two additional gravitational fundamental forces are mediated by gravitophotons (attractive gp and repulsive

gp ) as well as the quintessence particle (repulsive q dark energy). The quintessence particle q is assumed to

be responsible for the interaction between the spacetime field (vacuum field) and ordinary matter. The H1

Hermetry form for the graviton occurs in both tables, since gravitons can be generated by both ordinary matter as

well as by non-ordinary matter (Hermetry form H9 ), which is believed to be the case in the experiments Tajmar et

al. (2006 and 2008) The graviton field is equivalent to an acceleration field, which, in turn, is associated with inertia,

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i.e., Hermetry form H1 . Furthermore, the table contains three Hermetry forms marked by a * , which indicates that

some of the partial terms in its associated metric tensor are zero.

Table 1. Table of Hermetry forms for ordinary matter (OM) describing all messenger

particles (gauge bosons1), namely graviton, photon, vector bosons, and gluons as

well as all known types of matter (last three blue rows), i.e., leptons and quarks.

1The gauge bosons comprise the four known fundamental forces. However, these forces are not sufficient

to explain the experiments by Tajmar et al. (2006 and 2008) and Graham et al. (2007) (as was shown in

Dröscher and Hauser (2008)) nor can they account for dark matter or dark energy.

Table 2. Table of Hermetry forms for non-ordinary matter (NOM).

This table contains imaginary matter in the form of imaginary electrons and positrons (imaginary mass,

but real charge), which, however, are virtual particles, denoted as eI together with its messenger particle

I , where the existence of neutral leptons is postulated.

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Therefore, such a Hermetry form is designated as degenerated. Tables 1 and 2 provide a total of 16 Hermetry forms.

There is only one charged lepton for NOM, whose mass should be the electron mass. Comparison with the

corresponding Hermetry form H6 of charged leptons for OM shows that subspace R3 is missing. The presence of

R3 (cardinal number 3) seems to be responsible for the variety of different types of matter (cardinal number of T1 is

1 only). Subspace dimensions may play a role in computing the coupling constants (set algebra). Of particular

importance is the Hermetry form H15 (compare with Hermetry form H6 , which describes neutral leptons

e0 , 0 , 0 . Since they do not carry any electric charge they are not subject to electromagnetic interaction, and thus

cannot decay in the same way through the weak interaction as their charged counterparts, and hence might be stable.

Their masses could be close to those of the charged leptons. Thus, they could be candidates for dark matter. Their

interaction with ordinary matter is mediated through gravito-photons.

Imaginary Matter

The concept of imaginary matter in Table 2 should not be taken as if there existed a new type of matter (except for

the proposed neutral leptons, who might be associated with dark matter), since these particles are assumed to be

virtual particles of imaginary mass that is, they do not occur in the initial and final states of a reaction. They might,

however, act as a catalyst, enabling a novel interaction, namely the conversion of electromagnetic into gravitational

fields as seen in recent gravitomagnetic experiments. This means that all observed particle masses and charges are

still considered real. From Table 2 it can be seen that the neutral gravitophoton, gp (note that in Tables 1 and 2 the

neutral gravito-photon is denoted as 0

gp instead of gp ), can decay in two different ways. The first one, in which

the gp decay (see Figure 3) results in positive and negative gravitophotons, should produce a vertical gravity-like

field in the presence of an induced current in the superconducting rotating disk (Figure 5), caused by the external

magnetic induction field. The second decay scheme, giving a graviton and a quintessence particle, is assumed to

take place in the experiments by Tajmar et al. (2006 and 2008), when a circumferential gravity-like field in the plane

of the ring is produced by mechanically accelerating the cryogenic Nb ring.

In EHT, dark matter is composed of a new class of particles, the NOM: neutral leptons (fermions), but these are not

WIMPS (Weakly Interacting Massive Particles) whose masses are supposed to be hundreds of GeV, and thus have

elucidated present accelerators. The inertial masses of e0 , 0 , 0 have not been calculated, but are assumed to be

close to their charged counterparts, i.e., 0.511MeV c2 for electrons, 105.66MeV c2 , and 1.78GeV c2

(compared to 938MeV c2 for protons). Their gravitational interaction occurs, however, through the gravito-photon

field with coupling strengthGgp . The coupling between dark matter and ordinary matter therefore should be given

by GgGgp 1/ 67Gg .

Figure 3. Hermetry form H9 stands for the neutral gravitophoton gp produced by photon conversion, which can decay via two

different channels, depending on experimental conditions. The first one, upper branch, seems to take place in the

generation of the axial (vertical) acceleration field, called the Heim experiment. The second branch is assumed to occur

in the gravitomagnetic experiments by Tajmar et al. (2006, 2007a and 2007b) and Graham et al. (2007).

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If e0, 0, 0 existed in Nature, the question naturally arises: why did not accelerators already long ago produce these

particles? Accelerators or colliders produce beams of high-energy electrons or protons that are driven onto a target

or two beams are colliding from opposite directions. According to Table 1 and also in accordance with the Standard

Model, there is no place for OM neutral leptons, except for the almost massless neutrinos, which cannot contribute

more than 1 \% to dark matter. In EHT, however, the NOM counterpart to neutrinos, as can be seen from comparing

Tables 1 and 2, actually are the neutral leptons e0, 0, 0 .

Figure 4. In EHT, there exist two types of matter, OM (inner cube) and NOM (outer cube), which are represented each by eight

Hermetry forms, see Tables 1 and 2. Thus, the four-dimensional hypercube should represent all forms of matter that

do appear in the Universe.

In order to construct the physically meaningful set of metric sub-tensors that is, Hermetry (which stands for the

physical meaning of geometry, combined from hermeneutics and geometry) forms, it is postulated that

coordinates of internal spaces S2 (organization coordinates) or I2 (information coordinates) must be present

in any metric sub-tensor to generate a Hermetry form as stated in (Heim, 1977). 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 occurring in NOM, namely of the photon, gluon,

and dark matter. Hermetry form 16 is reserved for the inertia field. The interpretation of the meaning of Hermetry

forms was already given in Tables 1-4 of Dröscher and Hauser (2006), but has changed since then, based on new

physical facts derived from the interpretation of the experiments by Tajmar et al. (2006 and 2008) In Tables 1 and 2

Hermetry forms were also renumbered to better reflect their belonging to either OM or NOM.

Because of the double coordinate transformation underlying the construction of the polymetric tensor, see for

instance (Dröscher and Hauser, 2006 and 2005), any metric tensor describing a Hermetry form is composed of a

partial sum of metric terms, selected from the 64 components that comprise the complete polymetric tensor, which

in turn results from the inclusion of internal space H8 .

If space H8 is omitted, EHT is reduced to GR, and only gravitation remains. It is obvious that a double coordinate

transformation as employed in Dröscher and Hauser (2007) does not change, for instance, the curvature of a surface,

since it is an invariant (intrinsic to the surface). However, this fact is not relevant in the construction process of the

polymetric. The physical reason for the double transformation is to provide spacetime with the additional degrees of

freedom, expressed by the individual components of the metric tensor from which the various Hermetry forms are

constructed.

Only metric tensors representing Hermetry forms are of physical relevance, and it is clear from their construction

principle that all these tensors, derived from this underlying polymetric tensor, are different. Consequently, their

respective Gaussian curvatures K , where denotes the index of the corresponding Hermetry form, must also be

different. This is straightforward to observe, since Gaussian curvature is only a function of the first fundamental

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form (metric tensor components) as well as their first and second derivatives, but does not depend on the second

fundamental form. Therefore, each Hermetry form H determines its proper Gaussian curvature K , and thus

curves space according to its own specific metric. Following the rule of GR that interprets spacetime curvature as

gravitational interaction, the appropriate Hermetry forms are thus interpreted as physical interactions, as shown in

Tables 1 and 2.

Having established the qualitative physical relationship between Hermetry forms and spacetime curvature; all

physical interactions are connected to spacetime curvature, similar to GR, and thus physics has been geometrized.

Some additional remarks between the connection of geometry and physics are in place. Internal coordinates of

subspace R3 of Heim space H8 have dimension of length, and via the Compton wavelength are connected to mass,

and the internal coordinate of space T1 is responsible for charge. In Dröscher and Hauser (2006), it was already

shown that spacetime must be quantized at about the Planck length scale (maybe the length scale is somewhat

larger). Moreover, it is well known that in the case of gravitation in the Newtonian limit, metric element g00 (time

has coordinate index 0 in spacetime coordinates) is proportional to the gravitational potential equation.

EHT and Conservation Principles

The rocket principle requires that momentum is taken from the fuel and transferred to the space vehicle. According

to EHT, the space vehicle is acquiring velocity by imparting an equal and opposite momentum to the spacetime

field. A simple analogy is used to differentiate between the classical rocket principle (including all other means of

propulsion) and the novel field propulsion concept of EHT incorporating spacetime as a physical quantity.

Suppose a boat is in the middle of a large lake or ocean. In order to set the boat in motion, a force must be mediated

to the boat. The classical momentum principle requires that a person in the boat is throwing, for instance, bricks in

the opposite direction to push the boat forward. However, everybody is well aware of the fact that there is a much

better propulsion mechanism available. Instead of loading the boat with bricks, it is supplied with sculls, and by

rowing strongly the boat can be kept moving as long as rowing continues. The important point is that the medium

itself is being utilized, i.e., the water of the lake or ocean, which amounts to a completely different physical

mechanism. The rower transfers a tiny amount of momentum to the medium, but the boat experiences a substantial

amount of momentum to make it move. For space propulsion the medium is spacetime itself. Thus, if momentum

can be transferred to spacetime by field propulsion, a repulsive or recoil force would be acting on the space vehicle

moving it through the medium, like a rowing boat. The medium, spacetime, is a physical quantity, namely a field,

and if properly quantized, the respective particles mediating forces should also be present. Thus, in principle,

spacetime should have the capability to interact with a space vehicle. If this effect somehow can be experimentally

established, the principles of momentum and energy conservation require that the combined system, i.e., both

spacetime and space vehicle, are considered. According to EHT, this actually is the physical mechanism occurring in

the experiments by Tajmar et al. (2006 and 2008) and Graham et al. (2007) Important to note, this mechanism does

not extract momentum from the spacetime field and transfers it to the space vehicle. Instead, an active process has to

be triggered for the creation of gravito-photons, i.e., first generating a strong gravitomagnetic field, Bgp . Second, in

order to produce the gravity-like field seen in the experiments at AIT, experimental conditions have to be such that

the Bgp field can decay, producing gravitons and quintessence particles.

The important point is that in this scheme not only gravitons exist, but also gravito-photons as well as quintessence

particles. The important fact is that in the generation of the gravitomagnetic force via the decay of the gravitophoton,

as is assumed to be the case in the gravity-like experiments by Tajmar et al. (2006 and 2008), both the OM

(graviton, negative gravitational energy density) and NOM (quintessence particle positive gravitational energy

density) are generated, see Figure 3. The total energy in the generation of these two particles is therefore zero.

Gravitons interact with the space vehicle, i.e. they are absorbed by the space vehicle, while the quintessence

particles are reabsorbed by spacetime itself. This effect causes an acceleration of the space vehicle, while the

momentum of the quintessence particle is not felt by the space vehicle, but by the surrounding spacetime and leads

to its expansion, because of the repulsive force, and thus total momentum is being conserved. This effect is most

likely too small to be observed, but this kind of space propulsion should contribute to the expansion of the Universe.

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In the same way the momentum change of the ocean would not be discernible from the presence of a rowing boat.

Perhaps a local disturbance of spacetime might be measurable in the experiments by Tajmar et al. (2008)?

In the Heim experiment (vertical gravity-like field), see Figure 5, the neutral gravito-photon gp decays into the

positive gp and negative gp gravito-photons, Figure 3, which follows from the construction of the set of

Hermetry forms that, in turn, are a direct consequence of internal Heim space and its four subspaces. Again it is

assumed that the negative gravito-photons act on the spacecraft and the positive gravito-photons act on space such

that total momentum is conserved. As long as the experimental conditions for the production of gravito-photons

along with their respective decay are maintained, the proper acceleration field will be generated. For the same period

of time the interaction between space vehicle and surrounding spacetime remains. As soon as the gravito-photon

production and its subsequent decay stop, the acceleration field ceases to exist.

Field propulsion needs to interact with spacetime in order to work without propellant. The rocket principle is only

concerned with the energy and momentum balance of the physical system comprising the space vehicle and its fuel.

Therefore, regardless of the technology employed, this system is bound by the momentum that can be extracted from

the stored fuel. Therefore this principle, by definition, cannot produce a viable propulsion system delivering high

speed, long range, or high payload ratio.

An interesting question that so far has not been pondered is under what circumstances gravito-photons were or are

currently being produced on the cosmological scale and how this production might have influenced the expansion of

the Universe.

GRAVITATIONAL SPACE PROPULSION DEVICE

In the experiments by Tajmar et al. (2006, 2007a, 2007b and 2008) designed for the generation of gravity-like fields,

the gravitational force is acting in the plane of rotation in circumferential direction, opposing the original

mechanical acceleration of the ring or disk. The same holds true for GP-B, which was designed to measure the

Lense-Thirring effect.

Therefore, EHT was used to investigate whether a technically more convenient gravity-like field can be generated

whose force component is vertical, i.e., along the axis of rotation, while the rotation speed remains constant.

The experimental setup by Tajmar et al. (2006 and 2008) comprises an aluminum (Al) sample holder together with a

cryogenic rotating Nb ring fixed to the sample holder, which therefore is rotating at the same angular velocity. The

component in the z-direction, responsible for the acceleration field, is given by

; ; ;

ˆ 1 e ˆ ; ˆ sh (ˆ ˆ ) ˆ .

gp gp z Nb Al F gp gp z gp z

B k k k m g v B

m c

B ez ez g ez e ez e (10)

The factor comes from averaging over the area of the Al disk. The other constants have the following values:

k 3, kNb 1/ 20.49, kAl 1 denoting material constants, and F is the angular velocity of the imaginary electron

pairs derived from the Fermi energy where a value of vF 2.76105 m s was used. vsh denotes the mechanical

velocity of the rotating sample holder, and Bgp;z is the component of the gravito-photon field Bgp (dimension 1/s)

in the z -direction, see Figure 5. It should be noted that, in contrast to the acceleration field ggp , the magnitude of the

gravitomagnetic field Bgp should not depend on the mechanical angular velocity at which the Al sample holder and

Nb ring are moving. Experimental requirements for boson coupling are substantially lower than for fermion

coupling, which was calculated in Dröscher and Hauser (2004). It should be noted that for the gravitomagnetic field

generated in the experiments by Tajmar et al. (2006 and 2008) the term F should be replaced byNb , and thus a

dependence on the rotation speed of the Nb ring, at least within a certain range, should be observed.

According to current understanding, the (superconducting) solenoid of special material (red), see Figure 5, should

provide an imaginary magnetic induction field, in the z direction at the location of the rotating disk (gray), made

181

from a material different than the solenoid. The z -component of the gravito-photon field is responsible for the

gravitational field above the disk.

Figure 5. In this gravity-like field experiment the artificial gravitational field generated would be directed along the axis of

rotation. The second component is in azimuthal direction and should accelerate the ring or disk. Therefore, energy

needs not to be supplied to keep the angular velocity of the ring or disk constant. This experimental setup could serve

as field propulsion device, if a non-divergence free field were generated (the physical nature of the gravity-like field is

not known at present). The divergence of the field is believed to be different from zero.

This experimental setup could also serve as field propulsion device, if, as assumed, a non-divergence free field was

generated (the physical nature of the gravity-like field is not known at present), and if appropriately dimensioned.

Figure 5 describes the experimental setup utilizing a disk rotating directly above a (superconducting) solenoid. In the

field propulsion experiment of Figure 5, the gravito-photon force produces a gravitational force above the disk in the

z -direction.

The following assumptions were made for the experiment producing the vertical gravity-like field: N 10 , number

of turns of the solenoid, current of about 8 A (needed to calculate the component of the magnetic induction

field Bz ), diameter of solenoid 0.15 m , and rotation speed vsh 50 m s . The disk should be placed directly above

the solenoid to produce a magnetic field in z -direction only. This experiment should give an acceleration field of

about gp 6 10 2gˆ z ,

g e which is an appreciable field acting directly above the rotating disk. The value for the

achievable acceleration should show a resonance behavior and should be strongly material dependent. The cross

section area of the Nb ring should be larger than in the experiments by Tajmar et al. (2006 and 2008).

From these numbers it seems to be feasible that the realization of a space propulsion device that can lift itself from

the surface of the Earth is within current technological limits.

For a space vehicle with a total mass of 1.5105 kg and a desired acceleration of 1.3 g, a force of about 1.98106 N

is needed. Therefore, if a mass of 3.15103kg , is placed above the disk, i.e., is acting as charge in this acceleration

field, see Figure 5, such a force would be generated. Here it was assumed that the field is acting in the z-direction

and all of the mass sees the same acceleration field. In this regard, high-density material would be advantageous,

because of its smaller volume. Adding more mass would increase the force, which follows directly from Newton's

law. %In this regard, the ultimate propulsion system could be built, if matter from a neutron star could be used. This

follows directly from the fact that gravitation is represented by the curvature of spacetime and any mass located in

such a region would experience a force proportional to its mass. According to our calculations the acceleration field

is extending uniformly in the z-direction up to a height three times the radius of the disk, and after that should

assume a dipole character that is, the divergence of the field is different from zero. In order to generate the

acceleration field a rotation speed of 200 m/s, a coil of 1m diameter with 2,500 turns and a current of 8 A was

calculated, using, however, a different material than Nb. In addition, the material of the coil also should have an

influence on the strength of the acceleration field.

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All trip times given in Dröscher and Hauser (2004) remain unchanged, but as can be seen from the specifications

above, technical requirements were substantially reduced and should be feasible employing current technology. The

reason for this change is boson instead of fermion (vacuum polarization) coupling.

CONCLUSIONS AND FUTURE ACTIVITIES

Since 2002 ideas of a geometric approach for describing physical interactions, termed Extended Heim Theory

(EHT), were published. This approach predicts six fundamental physical interactions, three gravitational fields,

electromagnetism as well as the weak and strong interactions (Dröscher and Hauser, 2008, 2007b and 2006). In EHT

gravitation can be both attractive and repulsive. EHT also predicts the existence of virtual particles of imaginary

mass, responsible for the conversion of electromagnetic energy into gravitational energy. In addition to the existence

of ordinary matter (fermions and bosons), non-ordinary matter in the form of above virtual particles of imaginary

mass as well as stable neutral leptons should exist, which might be accountable for dark matter.

Numerous experiments by Tajmar et al. (2006, 2007a, 2007b and 2008) at AIT Seibersdorf carried out since 2003,

and first published in 2006, report on the laboratory generation of gravitomagnetic as well as gravity-like fields. The

gravitomagnetic effects measured were about 18 orders of magnitude larger than predicted by the so-called Lense-

Thirring effect of GR. In other words, the rotating niobium ring, having a mass of some 500 grams utilized by

Tajmar, produces a frame dragging effect similar to the mass of a white dwarf (Dröscher and Hauser, 2008). These

experiments were repeated by Graham et al. (2007), and more recently Tajmar et al. (2007b) provided a comparison

between the two experiments. If the experiments of Tajmar and Graham are correct, a similar effect should have

been observed in the NASA-Stanford Gravity-Probe B experiment as was calculated in Dröscher and Hauser (2009

and 2008). Indeed, a large gyro anomaly was observed in GP-B.

On the theoretical side EHT was used to analyze these experiments and also to approximately predict the magnitude

of the gyro misalignment in the GP-B experiment resulting from spin-spin interaction, caused by the generation of

gravity-like fields acting between the gyros in each of the two gyro pairs. The GB-P experiment utilized two

counter-rotating gyro pairs that, while in space, exhibited asymmetric misalignment, depending on the direction of

rotation. Theoretical predictions by EHT and measured misalignment were compared and gave reasonable

agreement. Hence, it remains to be seen whether the electrostatic patch effect, used in the post-flight analysis to

predict gyro misalignment by the Stanford team, is capable to completely account for both the magnitude and the

type of anomaly observed. According to EHT this anomaly should not be totally explainable by classical effects, i.e.,

electrostatic forces, etc. The Lense-Thirring (frame dragging) effect seems to exist exactly as predicted by GR.

Therefore, there is no room using a modification of the Lense-Thirring effect to explaining the large observed

gravitomagnetic fields.

In summary, the present situation is characterized by the fact that numerous experiments were performed over a

period of four years, employing different measurement techniques, showing similar, but unexpected results.

Measurement techniques in all experiments are clearly state of the art, in particular for the GP-B experiment.

Furthermore, gravity-like fields most likely would lead to novel technologies in the field of (space) transportation,

and thus should be of major interest to the public and to industry.

In addition, these fields might also be usable in several ways for clean energy generation leading, for instance, to

modified fusion energy research that could be highly relevant to the future, because a linear reactor geometry might

be feasible. In addition, several possibilities have been considered in generating electric energy directly from

gravity-like fields.

How to proceed? The experiments performed so far, if confirmed, will serve as demonstrators for the existence of

novel physical effects. However, in order to produce a propellantless space propulsion system, the experiment

generating a vertical gravity-like field needs to be carried out. According to EHT, the effect should be large enough

to be detectable with relatively simple measuring equipment, in contrast to the experiments performed so far, which

need extremely sensitive equipment to measure a small effect, and thus are susceptible to background noise.

Moreover, a vertical field might directly lead to some kind of gravity control. In particular the materials composition

of the disk and coil are of prime importance, since the magnitude of the vertical field seems to strongly depend on it.

183

A further significant question is, whether it will be possible to increase the critical temperature to room temperature

to avoid working with liquid He. Here it should be noted that even after more than 100 years of research,

superconductivity has elucidated a solution. Substantial theoretical efforts are needed both for a basic understanding

of the novel underlying physics as well as providing guidelines for revolutionary technologies.

ACKNOWLEDGMENTS

The assistance by M.Sc. O. Rybatzki, Faculty Karl-Scharfenberg, Univ. of Applied Sciences, Salzgitter Campus in

preparing the figures is gratefully acknowledged. The authors are grateful to Dr. M. Tajmar, AIT Seibersdorf,

Austria for providing measured data as well as for numerous comments regarding comparisons between EHT and

gravitomagnetic experiments. The authors are most grateful to Prof. P. Dr. Dr. A. Resch, director of the Institut fur

Grenzgebiete der Wissenschaft (IGW), Innsbruck, Austria for his support in writing this paper.

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