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SPACETIME PHYSICS AND ADVANCED PROPULSION CONCEPTS Revised Extended Version

02.05.2014 18:45

AIAA2006-4608LetterExtndVersionRevisedSept.pdf (5,1 MB)

AIAA 2006-4608

SPACETIME PHYSICS AND

ADVANCED PROPULSION CONCEPTS

Walter Dröscher1, Jochem Hauser1,2

1Institut für Grenzgebiete der Wissenschaft, Innsbruck, Austria

and

2Faculty Karl-Scharfenberg, University of Applied Sciences, Salzgitter, Germany

Revised Extended Version (20 Agust 2006)

Abstract: Spacetime physics includes general relativity (GR), quantum theory, quantum gravity, string theory (additional external

dimensions), and gauge theory (additional internal dimensions) as well as some modern variations. The paper will discuss the requirements

on future propulsion systems stemming from the demands for routine missions to LEO, the moon, or planetary missions

within the solar system, as well as interstellar flight. These requirements are compared with the limits imposed by the physical

laws of GR in conjunction with the physical theories listed above. The physical consequences of these field theories in

curved-spacetime as well as string and gauge theory, are discussed. Moreover, recent developments in the structure of spacetime

are presented, and their consequences for advanced propulsion systems are outlined. In particular, a novel experiment (ESA,

March 2006) reporting about the generation of an artificial gravitational field in the laboratory is discussed. This experiment, if

confirmed, could serve as the basis for a field propulsion device. Since a thorough understanding of the underlying physical principle

as provided by Extended Heim Theory (EHT) is of prevailing importance, both the theoretical and quantitative analysis of

this experiment are presented. Utilizing the experimental data along with the insight gained from theoretical considerations of

EHT, the concept for a field propulsion device is briefly outlined. Preliminary results of the propulsion capability of this device

are also given. Finally, an outlook on the necessary experimental and theoretical prerequisites is presented, to comprehend the

novel physics regarding the two different coupling mechanisms for fermions and bosons. Finally, the technical requirements for

such a propellantless propulsion device are briefly described.

1 Senior scientist, 2 Senior member AIAA, member SSE, © IGW, Innsbruck, Austria 2006

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1 Spacetime and Space Propulsion2

Space flight within the solar system requires the covering

of large distances. The distance to our moon is approximately

3.8×105 km, while Mars, our favorite destination is

about 0.5 A.U. away (astronomical units, 1 A.U. = 1.5×108

km). The next planet, Jupiter, is already 4 A.U. away from

Earth. The closest star is Proxima Centauri, which is 1.30

pc away from earth (parsec, 1pc = 3.3 ly) or, using a lightyear,

the distance light travels in the time of 1 year, (1 ly =

9.46×1012 km), it would take the light some 4.3 years to

reach this star. Expressed in miles, the distance is some 25

trillion miles from earth. The star closest to us which is

similar to our sun with respect to size and surface temperature

is Centauri, 1.33 pc away. But these distances are small

compared to the dimension of the Milky Way Galaxy

which comprises a galactic disk of about 100,000 ly in diameter

and 4,000 ly for the galactic bulge. Our solar system

is located some 8 kpc (kilo parsec) from the galactic center.

Our galaxy contains about 100 billion stars, and the

universe contains some 100 billion galaxies. The farthest of

these galaxies is approximately 13 billion ly away, which is

roughly the size of the observable universe. The age of the

Earth is estimated to be some 4.5 billion years, while there

are stars that are 7 to 10 billion years old. Having mentioned

both distance and time, the concept of spacetime has

been utilized and also, implicitly, the concept of metric has

been employed to measure distances in this four-dimensional

spacetime. This is the environment in which spaceflight

has to take place.

Next, we will briefly discuss our current capabilities3 to

travel through space and time. Current space transportation

systems are based on the principle of momentum generation,

regardless whether they are chemical, electric, plasmadynamic,

nuclear (fission) or fusion, antimatter, photonic

propulsion (relativistic) and photon driven (solar) sails, or

exotic Bussard fusion ramjets. Solar sails, nuclear explosions

(pusher, Orion), antimatter propulsion are most likely

in the realm of unfeasible technologies because of the large

engineering and/or safety problems as well as their prohibitively

high cost. The specific impulse achievable from thermal

systems ranges from some 500 s for advanced chemical

propellants (excluding free radicals or metastable atoms),

approximately 1,000 s for a fission solid-core rocket (NER2

Invited paper in the session 50-NFF-3 Faster Than Light, AIAA

42nd Joint Propulsion Conference, Sacramento, CA, 9-12 July

2006. Revision date 24 July and 20 August 2006. This paper supersedes

the original AIAA 2006-4608 Short Version as well as the

AIAA 2006-4608 Extended Version paper.

3 The cover picture shows a combination of two pictures. The first

one, taken from ref. [1], shows a view (artist's impression) from an

existing planet orbiting the solar-type star HD 222582 some 137 ly

away. The second one depicts the principle of the propulsion system

used to reach this planet, see Fig. 10.

VA program [2]) using hydrogen as propellant (for a gascore

nuclear rocket specific impulse could be 3,000 s or

higher but requiring very high pressures) up to 200,000 s

for a fusion rocket [3]. Although recently progress was reported

in the design of nuclear reactors for plasma propulsion

systems [4] such a multimegawatt reactor has a mass

of some 3×106 kg and, despite high specific impulse, has a

low thrust to mass ratio, and thus is most likely not capable

of lifting a vehicle from the surface of the earth. For fusion

propulsion, the gasdynamic mirror has been proposed as

highly efficient fusion rocket engine. However, recent experiments

revealed magnetohydrodynamic instabilities [5]

that make such a system questionable even from a physics

standpoint, since magnetohydrodynamic stability has been

the key issue in fusion for decades. The momentum principle

combined with the usage of fuel, because of its inherent

physical limitations, does not permit spaceflight to be carried

out as a matter of routine without substantial technical

expenditure. The above discussion does not even consider

the difficulties encountered when the simplicity of the

physical concept meets the complexities of the workable

propulsion system.

At relativistic speeds, Lorentz transformation replaces Galilei

transformation where the rest mass of the propellant is

multiplied by the factor (1 - v2/c2)-1 that goes to infinity if

the exhaust velocity v equals c, the speed of light in vacuum.

For instance, a flight to the nearest star at a velocity of

some 16 km/s would take about 80,000 years. If the speed

of light cannot be transcended, interstellar travel is impossible.

We conclude with a phrase from the recent book on future

propulsion by Czysz and Bruno [6] : If that remains

the case, we are trapped within the environs of our Solar

System. In other words, the technology of spaceflight

needs to be based on novel physics that provides a novel

propulsion principle.

In addition, this discussion leads us to conclude that the

current state of propulsion neither permits comfortable

flights to other planetary systems nor to our moon. Even

the achievement of a Low Earth Orbit will remain a laborious,

dangerous and extremely costly procedure with this

technology. In the long run this technology will inflict prohibitively

high cost and risk for all kind of space missions.

This is not because the technology is insufficiently advanced,

but the underlying physical principles do not allow

efficient and effective as well as safe space travel. Although

advanced propulsion concepts as described above

must be pursued further, a research program to look for

fundamentally different propulsion principles is both

needed and justified, especially in the light of the recent experiment

by Tajmar et al. [7], and also because ideas for a

fundamental physical theory predicting additional physical

interactions recently became more concrete and realistic,

for instance, [8], [9]. In Sec. 4 this theory will be used to

calculate Tajmar's experiment and to provide guidelines for

a modified experiment that would serve as demonstrator for

a propellantless propulsion device.

As mentioned by Krauss [10], general relativity (GR) allows

metric engineering, including the so-called warp

drive, see Sec. 2.2, but superluminal travel would require

negative energy densities. Furthermore, in order to tell

space to contract (warp), a signal is necessary that, in turn,

can travel only with the speed of light. GR therefore does

not allow this kind of travel.

On the other hand, current physics is far from providing final

answers. First, there is no unified theory that combines

GR and QM (quantum mechanics). Second, not even the

question about the total number of fundamental physical

interactions can be answered. Hence, the goal to find a

unified field theory is a viable undertaking, because it

might lead to novel physics, which, in turn, might allow for

a totally different principle in space transportation4. The

only solution for an advanced propulsion system lies in the

detection of those hitherto unknown physical laws. As has

been discussed above and will be outlined further in Sec. 7,

there exists credible experimental evidence in conjunction

with a theoretical framework for these laws to exist

which may lead to the construction of a technically feasible

propulsion device. This propulsion principle would be far

superior compared to any device based on momentum

generation from fuel, and would also result in a much simpler,

far cheaper, and much more reliable technology.

Such a technology would revolutionize the whole area of

transportation.

2 Classical Spacetime

Since any space vehicle is flying through spacetime, the nature

and properties of spacetime should be thoroughly understood,

because they may eventually be the key for an advanced

space propulsion mechanism. As we will see, the

nature of spacetime is not obvious and the classical point of

view, see below, does not represent the physical facts. The

physical consequences, however, have not yet been fully

worked out.

In GR the model of space and time supports continuous and

differentiable functions and provides a structure that has the

same local topology as ℝ4. Therefore, spacetime is a topological

space and thus comprises a collection of open sets.

For small regions it is assumed that the open sets possess

the topology of ℝ4. Therefore, a one-to-one mapping exists

between the open set of spacetime and ℝ4. Each point in

spacetime has a unique image in ℝ4 and vice versa.

2.1 Spacetime as a Manifold

Equipped with the features described above, spacetime is

called a manifold. In general, physical fields defined on an

open set of this manifold are assumed to be differentiable.

4 A more detailed discussion will be given in our paper entitled Field

Propulsion I: Novel Concepts for Space Propulsion.

Spacetime thus is considered to be a multiply differentiable

manifold. However, as will be shown in Sec. 4, space- time

must be quantized. Therefore, it is not generally possible to

have a third point between any two points in spacetime.

Spacetime is not dense and hence the concept of manifold

is incorrect, at least on the Planck length scale. In SRT (special

theory of relativity) Lorentz contraction is continuous,

but this contradicts the concept of minimum length.

At Planck scales SRT cannot be correct. GR uses the concept

of curvature, but at Planck scales it cannot be measured

exactly. This is equivalent to fluctuations of curvature

and thus of gravitation itself. A unified field theory describing

all physical interactions by a set of individual metric

tensors would be subject to fluctuations as well that is,

all physical forces would be subject to these fluctuations.

Physics in the way we know it is not possible below the

Planck scale, since concepts of metric, dimensionality, or

points are not defined. Spacetime itself is a field and thus

needs to be quantized, leading to quantum gravity (QG),

see, for instance [11]. So far, QG has not lead to a unified

field theory, and does not predict any phenomena that

could lead to a novel propulsion concept. The same holds

true for String theory, for instance [2] that does not make

any testable predictions at all. Conventional wisdom claims

that quantized spacetime acts on the Planck scale only. On

macroscopic scales the concepts of GR are sufficient to describe

spacetime. However, this argument may turn out to

be invalid, since despite the smallness of the quantized action,

denoted by the Planck constant h, physical phenomena

on the macroscopic scale do occur, for instance superconducting

and condensed matter phenomena [12]. Therefore,

it is conceivable that a quantized spacetime may lead to

novel observable physical phenomena. For instance, quantized

spacetime together with the prediction of a repulsive

gravitational force, predicted by EHT, see quintessence

particle in Table 1, leads to the concept of a covariant

(physical equations remain form invariant) hyperspace (or

parallelspace), in which the limiting speed of light is nc,

with n > 1 integer, and c the vacuum speed of light [13],

[14]. As was shown in these papers, conditions can be derived

under which, at least theoretically, material objects

might enter and leave hyperspace. These conditions were

obtained from a coupling mechanism based on vacuum polarization

involving virtual electrons (fermions, particles

with half-integer spin). So far, no investigations were made

to determine whether these conditions would change in

the light of Tajmar's experiment that takes place in a condensed

matter environment and involves the coupling to

bosons (particles with integer spin, Cooper pairs in superconducting).

2.2 The Physics of Continuous Spacetime

Einsteinian spacetime [15], [16] is indefinitely divisible

and can be described by a differentiable manifold. In reality,

however, spacetime is a quantized field. Gravitation is

the dominant force in systems on astronomical scales. GR

can be summarized in the single sentence: matter curves

spacetime. For a flat geometry, the angles of a triangle add

up to 180 degrees. For a generally curved spacetime the

metric is written in the form (double indices are summed

over)

ds2=gdxdx (1)

where g is the metric, x1, x2, x3 are the spatial coordinates,

and x4 is the time coordinate5. Einstein summation

convention is used, i.e., indices occurring twice are

summed over. The following metric examples are considered

in increasing complexity.

The spacetime metric of a flat universe is given by

ds2=dx2dy2dz2−c2 dt2 .

Presently it is assumed that the observable Universe is flat,

see Fig 1. It still can be closed, see for instance [17]. Since

we reject the idea of infinities in physics, because they contradict

the quantization principle, the Universe should not

be open [18].

On the surface of a sphere spherical coordinates are used

ds2=dr2r2 d 2r2 sin2d 2−c2 dt2 .

The cosmological principle states that the Universe does

not have preferred locations (homogeneous) or directions

(isotropic). Therefore the spatial part of the metric has constant

curvature. Extending the spherical metric, the most

general metric is given by the Robertson-Walker metric

ds2=a2t [ dr2

1−k r2r2d 2sin2 d2]−c2dt2 ,

where a(t) is the scale factor for an expanding Universe.

Here it is assumed that the Universe started from a fixed

size x0 and expanded according to a(t). Two points that

were at distance x0 at time t0, now are at distance x(t)

= a(t) x0. This is a cosmological model with a radially symmetric

metric tensor, and a function a(t) that acts as the radius

of the universe.

In 1994 Alcubierre [19], [20] specified the following metric,

termed the warp-drive spacetime

ds2=[dx−V s t f rs dt]2dy2dz2−c2 dt2 ,

where Vs(t) is the velocity along a given curve xs(t) 6 and

rs(t) = (x-xs(t))2 + y2 + z2. A choice for fs(t) is fs = (1-rs/R)4

and R is a distance. Without proof it is stated that, if this

warp-drive metric could be generated - the term metric engineering

was coined - around a spaceship, the vehicle

would be traveling faster than the speed of light, seen from

a spacetime diagram of flat space. Locally the ship is moving

less than the speed of light. A bubble of spacetime curvature

must surround the spaceship. Since the Alcubierre

metric requires a negative local energy density, it cannot

work in GR. Quantum mechanics allows negative energy

5 Often the time coordinate is denoted as x0.

6 For simplicity y = 0 and z = 0 are assumed.

density, and perhaps a combination with the quintessence

particle, see Fig. 3, the sixth fundamental force predicted

by EHT provides a theoretical framework. It is interesting

to note that the experiment by Tajmar et al. [21] could be

interpreted as metric engineering, since an artificial gravitational

field was generated and, as a result, the local metric

has been changed.

There are also spacetime concepts of higher dimensionality.

Kaluza (1921) introduced an additional fourth spatial dimension

into Einstein's field equations, and in a letter to

Einstein pointed out that Maxwell's theory of electromagnetism

was comprised in the now 5-dimensional Einstein

equations. However, his theory produced divergencies and

could not answer the question about the visibility of this 5th

dimension. In 1926 Klein, a Swedish physicist, introduced

the concept of a curled up dimension that exists on the

Planck length scale only, and thus cannot be observed by

experiment. String theory, for instance [22], see Sec. 5, has

extended this concept by introducing 7 additional spatial

dimensions, resulting in a total of 10 spatial an 1 time dimensions.

3 Symmetries in Classical Spacetime

Symmetries (beauty) have a fundamental role in classical

and modern physics. They completely determine the physics.

Eventually all symmetries are a feature of the underlying

physical space which is the combination of spacetime

and an additional internal or external space. Any physical

law is based on a corresponding symmetry. Therefore

physical space should be the generator of all physical interactions

and this should be reflected by any physical theory.

Symmetry means that one can transform the object in some

way, so that it appears unchanged after the transformation.

In other words if there is an invariance under transformation

or symmetry the respective feature is unobservable.

If in a mirror image a systems looks the same, the system

possesses reflection symmetry. There is also invariance under

rotation, for example if the system is a soccer ball. The

difference between these two symmetries is that the first

one is discrete and the second one is continuous, i.e., the rotation

angle varies continuously between 0 and 2π. In classical

physics the Lagrange function of a system,

Lx , ˙x , t , is the object whose symmetry properties are

investigated with respect to the homogeneity and isotropy

of space as well as the homogeneity of time. Invariance under

translation, leads to momentum conservation. Invariance

in time translation results in energy conservation and

invariance under rotation is responsible for conservation of

classical angular momentum [23].

In general, Noether's theorem says that if the equations of

motion (Euler-Lagrange, which follow from the variation

of the Lagrange function) are invariant under a transformation,

then there exists an integral of motion, i.e., a conserved

quantity. The symmetry concept also holds for the

Lagrange function describing electromagnetism. These

simple considerations show the fundamental role of spacetime.

All classical physics follows from the geometry and

topology of spacetime as a manifold. However, as will be

shown in the next chapter, spacetime is not a manifold nor

a set of points, but a fluctuating field. Moreover, in the fifties

of the last century it was shown by experiment that

there are additional discrete symmetries that are not conserved.

For instance, reversing the spatial coordinates that

is, doing a space parity transformation, should not change

the physics. Empty space does, however, distinguish between

left and right. Some elementary particles are lefthanded

in their interaction. This is a clear sign that particles

may have more degrees of freedom, and thus looking at an

elementary particle in spacetime only does not reveal all its

physical information. Therefore, physical space needs to

be considered that contains the complete set of information

for a particle containing spacetime as a subset. Spacetime

could either be part of a higher dimensional space with additional

spatial coordinates, or at each point in spacetime,

an additional internal space must exist that accounts for the

additional degrees of freedom.

4 Quantized Spacetime

In the following it is shown that the combination of quantum

theory (Heisenberg's uncertainty relation) with special

relativity (constancy of the speed of light and E = mc2)

and general relativity (Schwarzschild radius) directly

leads to a quantized spacetime, resulting in the well

known Planck scales. The proof is straightforward and is

given below. The quantization of spacetime in conjunction

with the sixth interaction of EHT, repulsive gravitation, see

Sec. 6, leads to the proposition of a hyperspace (parallel

space) in which superluminal speeds should be possible, as

was shown in [24].

Heisenberg´s indeterminacy (uncertainty) relation, for instance

relating time and energy indeterminacies,

tEℏ , allows for arbitrarily small Δt by making

the energy uncertainty arbitrarily large. However, this is not

the case in the real physical world. It is straightforward to

prove the discreteness of spacetime. To prove the discrete

nature of spacetime, the time measurement process using

clocks is analyzed [25] Einstein's GR itself is used to disprove

the existence of continuous spacetime. According to

Einstein, the energy of any material object is E = mc2. The

smallest time interval, δt, that can be measured must of

course be larger than the time uncertainty required to satisfy

Heisenberg's uncertainty relation that is

tt=ℏ/E . A clock of mass m cannot have an energy

uncertainty ΔE > mc2, because this would lead to the

creation of additional clocks, hence  tt=ℏ/mc2 . A

clock of length l needs a measuring time c δt > l in order to

receive the measuring signal. A characteristic length of a

material body is its Schwarzschild radius, namely when its

gravitational energy equals its total energy mc2, i.e., rS =

Gm/c2. This means for the mass of the clock m < rS c2/G,

because the body must not be a black hole from which signals

cannot escape. Inserting the value l for rS , m < δt

c3/G. Inserting the value of m in the above relation for δt,

one obtains the final relation t2ℏG/c5. Thus the

quantization aspect of the GODQ principle, see the following

section, directly delivers a fundamental lowest limit for

a time interval, termed the Planck time. In a similar way the

smallest units for length and mass can be found. As shown

above, Planck units are constructed from the three fundamental

constants in Nature, namely ћ, c, and G. The values

for the Planck units are:

• Planck mass mp = (ћc/G)1/2 = 2.176´10-8 kg,

• Planck length lp = (Gћ/c3)1/2 = 1.615´10-35 m,

• Planck time tp = (Gћ /c5)1/2 = 5.389´10-44 s.

This means that the classical picture of points in a continuous

spacetime does not make physical sense (this also applies

to Feynman diagrams). Physics below the Planck units

must be totally different, since one cannot distinguish between

vacuum and matter. No measurements are possible.

The nature of spacetime is discrete in the same way as energy

is discrete, expressed by E = h. Therefore spacetime is

a quantum field, and it should have corresponding quantum

states, described by a quantum field theory. Since spacetime

is equivalent to gravity, gravity itself needs to be described

by a quantum field theory. In both classical physics

and quantum mechanics point particles are used, and the inverse

force law leads to infinities of type 1/0 at the location

of the particle. As was shown above, any particle must have

a discrete geometric structure, since it is finite in size. The

minimal surface must be proportional to the Planck length

squared. From scattering experiments, however, it is known

that many particles have a much larger radius, for instance,

the proton radius is some 10-15 m, and thus its surface

Figure 1: This picture, taken from Wikipedia, shows

three types of possible geometries for the Universe,

namely closed, open, or flat. At present, a flat Universe

is assumed (that means the part that can be observed appears

flat, i.e., whose redshift is smaller than the speed

of light c in vacuum). This only means that the Universe

is very large [17].

would be covered by about 1040 elemental Planck surfaces.

Hence, an elementary particle would be a highly complex

geometrical structure. Heim [26], [27] has analyzed

in detail the structure of elementary particles and introduced

the concept of a smallest surface termed Metron.

According to Heim, the current area of a Metron, , is

3Gh/8c3 .

The Metron size is a phenomenologically derived quantity

and is not postulated. It is therefore mandatory that point

particles are banished conceptually.

5 Spacetime of Higher Spatial Dimensions:

String Theory

Novel physics most likely comes from a unified theory.

Over the last five decades many attempts have been made.

No successful theory has emerged so far. One of the most

prominent recent theories is String theory which uses ideas

from Kaluza and Klein. The theory by Kaluza and Klein

(1921, 1926) already introduced a fourth spatial dimension

to account for electromagnetism. There is nothing in Einstein's

theory to forbid the introduction of additional coordinates.

According to string theory, electrons are not point

particles, but are vibrations of a string, whose length is at

the Planck scale, some 10-35 m. Strings are one-dimensional

entities. Sounding these strings they can turn into other particles,

for instance, the electron can turn into a neutrino, or

into any of the known subatomic particles. String theory

leads to a unification of the four fundamental interactions,

but requires more spatial dimensions. However, because of

the discrete nature of spacetime there seems to be no need

for string theory, which replaces point particles by strings,

but requires hitherto unobserved additional spatial dimensions.

6 Gauge Theory as Spacetime with Internal

Dimensions

However, there is a fundamental difference compared to the

concept of spacetime with internal dimensions, in that

strings are objects in spacetime, while in this section a geometrization

concept is employed that explains all particles

as geometric objects constructed from spacetime itself.

There exists another concept, coming from the idea that elementary

particles have additional degrees of freedom in

some kind of internal space. Therefore, the concept of

physical space as the combination of spacetime and internal

space is introduced. This marriage of 4-dimensional spacetime

with internal space is called fiber bundle space mathematically.

In the following the term physical space will be

used for this combination, since all the fundamental forces

of physics will be described in this space. These internal

degrees of freedom can then be connected with the dynamical

motion in spacetime. This is the geometrical structure

utilized in gauge theory. The dimension of the internal

space and its symmetries determine the physics that is possible.

In order to have a unified field theory the proper internal

space has to be constructed that encompasses all interactions

of physics. In the next section, GR is equipped

with an 8-dimensional internal space, termed Heim space.

Once this internal space is set up, all physical interactions

are fixed. There is only one single selection rule for building

internal subspaces that have physical meaning, see below.

It turns out that six fundamental physical interactions

should exist.

6.1 Special Gauge Theory: Extended Heim

Theory

In EHT a set of 8 additional coordinates is introduced, but

contrary to String theory, the theory postulates an internal

space with 8 dimensions that governs physical events in

our spacetime (actually a curved 4D manifold M).The crucial

point lies in the construction of the internal space that

should come from basic physical assumptions, which must

be generally acceptable. In EHT, an 8-dimensional space is

constructed, termed Heim space, H8 that is missing in GR.

In other words, GR does not possess any internal space, and

thus has a very limited geometrical structure, namely that

of pure spacetime. Because of this limitation, GR cannot

describe the fundamental forces in physics and consequently

has to be extended. The extension as done in EHT, lies in

the introduction of the internal space H8. EHT reduces to

GR when this internal space is omitted. The metric tensor,

as used in GR, has purely geometrical means that 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. Stated in simple terms: matter

curves spacetime. In this way, the metric tensor field has

Figure 2: In gauge theory particles have additional degrees

of freedom, expressed by an internal space. The horizontal

plane depicts spacetime, the vertical axis denotes internal

space. In this sense EHT can be considered as a gauge theory

where an 8-dimensional internal space is constructed at

each point in spacetime, forming a fiber bundle space. All internal

coordinates, except the spatial energy coordinates

(mass), have negative signature. In EHT no additional external

spatial coordinates exist. It remains to specify the proper

gauge potentials and the corresponding Lagrange densities

for describing the fundamental interactions in EHT.

Time

Space

Internal Space

become a physical object whose behavior is governed by an

action principle, like that of other physical entities.

According to the quantization principle, the minimal length

in the space part of H8 is the Planck length. Applying the

geometrization rule of the GODQ principle, see next paragraph,

Planck mass and Planck time are converted into

length units leading to two additional lengths constants lpm

= ℏℏ /mpc and lpt = ctp that have the same numerical value

as lp but define two additional different length scales, relating

lengths with time units as well as length with mass

units. The introduction of basic physical units is in contradiction

to classical physics that allows infinite divisibility.

As a consequence, measurements in classical physics are

impossible, since units cannot be defined. Consequently,

Nature could not provide any elemental building blocks to

construct higher organized structures, which is inconsistent

with observation. Thus the quantization principle is fundamental

for the existence of physical objects. Therefore the

three Planck length units as defined above must occur in

the structure of both spacetime and internal space H8. In

spacetime length unit lp is the basic unit for the spatial coordinates

and lpt measures the time coordinate. In order to

connect geometry with physical entities, in the internal

symmetry space coordinates i are measured in units of

lpm . Hence all lengths in H8 are represented by multiples of

1/mp, and therefore internal coordinates i with i =

1,...,8 are denoted as energy coordinates. In other words,

the concept of energy coordinate ensures that an inverse

length is representing a physical mass. Since length values

are quantized, the same holds for physical mass. In this regard

the connection of geometry with physical objects has

been established, but, in order to achieve this goal, the

quantization principle had to be introduced ab initio.

In contrast to Einstein, EHT is based on the following four

simple and general principles, termed the GODQ principle

of Nature7.

i. Geometrization principle for all physical interactions,

ii. Optimization (Nature employs an extremum

principle),

iii. Dualization (duality, symmetry) principle (Nature

dualizes or is asymmetric, bits),

iv. Quantization principle (Nature uses integers

only, discrete quantities).

From the duality principle, the existence of additional internal

symmetries in Nature is deduced, and thus a higher dimensional

internal symmetry space should exist, termed

Heim space H8, which will now be determined.

In GR there exists a four dimensional spacetime, comprising

three spatial coordinates, x1, x2, x3 with positive signature

(+) and the time coordinate x4 with negative signature

7 This will be discussed in detail in our forthcoming paper: Field

propulsion I: Novel Physical Concepts for Space Propulsion.

(-). It should be remembered that the Lorentzian metric of

ℝ4 (actually spacetime is a manifold M) has three spatial

(+ signature) and one time-like coordinate (- signature)8.

The plus and minus signs refer to the local Minkowski metric

(diagonal metric tensor, see Eq. (1)). Therefore, the

squared proper time interval is taken to be positive if the

separation of two events is less than their spatial distance

divided by c. Hence a general coordinate system in a spacetime

manifold M (locally ℝ4) comprises the curvilinear coordinates

ημ with μ = 1,..,4 and η = ημ ∈ M where η denotes

an element (point) of M.

The set of 8 internal coordinates is determined by utilizing

the GODQ principle introduced above. The three internal

spatial coordinates 1 ,2 ,3 are associated with Planck

length lpm, the internal time coordinate 4 with lpt. The

other four coordinates are introduced to describing the degree

of organization and information exchange as observed

in Nature. To this end, the second law of thermodynamics

is considered, which predicts the increase of entropy. Although

negative entropies are possible, they cannot account

for the high degree of organization prevailing in Nature.

The second law of thermodynamics says something about

the direction of a process, but will not lead to highly organized

structures by itself. Everywhere in Nature, however,

highly organized structures can be found like galaxies, solar

systems, planets, plants etc., which, according to the duality

principle, have to be introduced into a unified theory.

We are referring to the article of P.W. Anderson More is

Different [28]. It simply says that the ability to reduce everything

to its basic constituents and fundamental laws

does not imply the ability to start from these laws and reconstruct

the phenomena, i.e., the Universe. In that sense,

these coordinates express some kind of a collective behavior,

which is reflected by the entelechial and aeonic coordinates,

see below. A description of Nature that only provides

a route to decay or to lower organizational structures is in

contradiction to observation.

Therefore, an additional, internal (negative signature -) coordinate,

termed entelechial coordinate, 5 , is introduced.

The entelechial dimension can be interpreted as a

measure of the quality of time varying organizational

structure (inverse or dual to entropy). It should be mentioned

that all other additional internal coordinates have

negative signature, too. When the Universe was set into

motion, it followed a path marked by a state of great order.

Therefore, to reflect this generic behavior in Nature, the aeonic

dimension, 6 , is introduced that is interpreted as a

steering coordinate toward a dynamically stable state.

On the other hand, the entropy principle is firmly established

in physics, for instance in - decay.

8 Normally the time coordinate is denoted as x0. Because of the additional

coordinates with negative signature this convention is not

useful. The signature signs are convention only and can be reversed.

Entropy is directly connected to probability, which in turn

is related to information. Therefore, two additional coordinates

7 ,8 are needed, which are complementary to the

organizational coordinates, to reflect this behavior of Nature,

termed information coordinates that are describing

information waves. Finally, a connection from geometry

(space and time) to physics (mass) has to be established 9.

Since space and time coordinates are associated with

Planck length scales, see above, they provide the connection

between geometry and mass via the Compton wave

length and thus are present in H8.

9 Tables of hermetry forms and their physical meaning are also described

in the brief introduction to EHT, which can be downloaded from

www.hpcc-space.com.

In summary, internal coordinates i with i=1,, 4

denote spatial and temporal coordinates, i with

i=5,6 denote entelechial and aeonic coordinates, and

i with i=7,8 denote two information coordinates in

H8, mandating four sets of types of coordinates.

With the introduction of a set of four different types of coordinates,

the space of fundamental symmetries of internal

space H8 has been fixed. The theoretical framework is

provided in Sec. 5 where a set of metric subtensors is constructed,

each of them describing a physical interaction or

particle. Thus the connection between physical space and

physics (symmetries) is established in exactly the way as

Six Fundamental Physical Forces

Gravitation

Electromagnetic Weak Strong

Gravitation Gravitation

Gravitophotons H5(S2 x I2)?

attractive +, repulsive -

Ggp = 1/672 Gg

Graviton H1(S2)?

attractive +

Gg = 6.671 x 10-11 Nm2/kg2

Quintessence H9(I2)?

repulsive -

Gq = 4.3565 x 10-18 Gg

Coupling of

Electromagnetism - Gravitation

Virtual particles:

Nuclear Force ??

Photon

Atoms

Light

Chemistry

Electronics

Real matter:

Solar System

Galaxies

Black holes

Bosons Gluons

Baryons

Mesons

Nuclei

Neutron decay

Beta radioactivity

Neutrino interaction

Stellar fusion

W+ W- Z

Dark energy

Cosmic acceleration

photon

Ggp

 Ggp

−

Figure 3: EHT predicts, as one of its most important consequences, two additional, gravitational like interactions and the existence

of two messenger particles, termed gravitophoton and quintessence. That is, there is a total of six fundamental physical

interactions. The name gravitophoton has been chosen because of the type of interaction, namely a transformation of the electromagnetic

field (photon) into the gravitational field (gravitophoton). The arrow between the gravitophoton and electromagnetic

boxes indicates the interaction between these messenger particles that is, photons can be transformed into gravitophotons.

In the same way the quintessence interaction can be generated from gravitons and positive gravitophotons (repulsive force)

where it is assumed that first a neutral gravitophoton is generated that decays into a pair of negative (same sign as gravitational

potential) and positive gravitophotons.

foreseen by Einstein. Physical space is responsible for all

physical interactions. However, in order to reach this objective,

spacetime had to be complemented by internal space

H8. This is the novel aspect in EHT, which otherwise is

based on the well known concept of gauge theory. Once the

internal space with its sets of coordinates has been determined,

everything else is fixed because Eq. 2 is nothing but

the direct extension of GR provided with an internal space.

The relationship between the mappings of GR and EHT

follows from the comparison of Figs. 4 and 7.

In order to construct a hermetry form, either internal space

S2 or I2 must be present. In addition, there are three degenerated

hermetry forms that describe partial forms of the

photon and the quintessence potential, for details see Table

4. They allow the conversion of a photon into a gravitophoton

(gravitation can be both attractive and repulsive) as

well as of gravitophotons and gravitons into quintessence

(gravitation is repulsive) particles. It should be noted that a

dimensional law can be derived that does not permit the

construction of, for instance, a space H7. Heim space, H8 ,

comprises four subspaces, denoted as R3, T1, S2, and I2. Fig.

(7) shows the set of metric-subspaces that can be constructed,

where each admissible metric subtensor is denoted as

hermetry form. 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. [13],

[29].

6.1.1 The Physics of Hermetry Forms

The four tables, Tables 1-4, contain the complete set of

hermetry forms (individual metric tensors) and their associated

physical meaning. It is most important to note that

gravitation comprises three interactions that are mediated

by three messenger particles, termed graviton (attractive),

gravitophoton (attractive and repulsive), and quintessence

(repulsive) particle. The gravitophoton interacts with virtual

matter, while the quintessence particle interacts with the

vacuum.

6.1.2 Hermetry Forms and Physical Interactions

The concept of an internal 8D space comprising four subsets,

leads to a modification of the general transformation

being used in GR. The existence of the internal space requires

a double transformation as shown in Fig. 5. Each of

the 15 admissible combinations of metric subtensors (hermetry

forms) is ascribed a physical meaning, see Fig.7 and

Tables 1-4.

In EHT therefore a double transformation involving Heim

space H8 occurs, see Eq. (2). This global metric tensor does

not have any physical meaning by itself, instead by deleting

corresponding terms in Eq. () eventually leads to the metric

of the proper hermetry form10.

gi k=∂ xm

∂

∂i

∂ xm

∂

∂k

(2)

As described in [9], [24] there is a general coordinate transformation

xmi  from M (locally ℝ4) H8 N (locally

ℝ4) resulting in the polymetric metric tensor, see

Figs. 5 and 7.

10 A more complete discussion can be found in refs. [9], [24].

Figure 4: In GR the metric tensor is computed using a mapping

from manifold M (curvilinear coordinates ηl ) to manifold N in

flat spacetime (locally) ℝ4 (Euclidean coordinates are denoted by

xm). Calculating the components of the metric tensor as well as

lengths, areas, and volumes from the metric tensor, a mapping to

the set of real numbers is needed. This kind of mapping delivers

one single type of monometric tensor that is responsible for

gravity only, appearing on the LHS of the Einstein field equations.

Figure 5: Einstein's goal was the unification of all physical interactions

based on his principle of geometrization, i.e., having a

metric that is responsible for the interaction. This principle is

termed Einstein's geometrization principle of physics (EGP). In

order to obtain all physical interactions, the concept of an internal

space, denoted by the authors as Heim space H8, having 8 internal

dimensions, is introduced. These invisible internal coordinates

govern events in spacetime. Therefore, a mapping from manifold

M (curvilinear coordinates ηl )in spacetime to internal space H8

and back to manifold N in spacetime must be used to properly describe

the physics. This is a major deviation from GR and leads to

a polymetric tensor. EHT contains GR as a special case.

where indices α, β = 1,...,8 and i, m, k = 1,...,4. The Einstein

summation convention is used that is, indices occurring

twice are summed over. It is clear from Eq. 2 that GR is a

special case of EHT. If Heim space were not existing, the

polymetric of EHT collapsed to the monometric of GR.

A particular component of the metric tensor belonging to

one of the four subspaces is given by Eq. (3).

Because of the double transformation each component of

the metric tensor in spacetime can be written as the sum of

64 subcomponents, Eq. (4). Each hermetry form is marked

by the fact that only a subset of the 64 components is present.

This means that certain components are 0 for a given

hermetry form. Therefore each hermetry form leads to a

different metric in the spacetime manifold and thus describes

different physics. This is why Eqs. (5) represent a

polymetric.

gi k

= ∂ xm

∂

∂ 

∂i

∂ xm

∂

∂k .

(3)

gi k= Σ

 ,=1

gi k

 (4)

gi k Hℓ =: Σ

 ,∈H ℓ

gi k



(5)

Twelve hermetry forms can be generated having direct

physical meaning, by constructing specific combinations

from the four subspaces. The following denotation for the

metric describing hermetry form Hℓ with ℓ=1,...,12 is used.

Summation indices are obtained from the definition of the

hermetry forms, see Fig. 7 and Table 2.

The expressions gi k H ℓ  are interpreted as different

physical interaction potentials caused by hermetry form

Hℓ, extending the interpretation of metric employed in GR

to the polymetric obtained from the complete physical

space that is, the combination of internal space of H8 with

four-dimensional spacetime M.

Internal space H8 is a factored space that is H8

= R3×T1×S2×I2. The factorization into one space-like manifold

R3 and three time-like manifolds T1, S2 and I2 is inherent

to the structure of H8. For the construction of the individual

hermetry forms, a selection rule is used, namely any physically

meaningful hermetry form must contain space S2 or

I2.

Each individual hermetry form is equivalent to a physical

potential or a messenger particle. It should be noted that

hermetry forms in spaces S2×I2 describe gravitophotons,

and spaces S2×I2×T1 are representing photons, see Table

2. This is an indication that, at least on theoretical arguments,

photons can be converted into gravitophotons, if the

time dependent part T1 of the photon metric can be canceled.

How this can be achieved experimentally will be outlined

in Sec. 7.

Figure 6: There should be three gravitational particles, namely

the graviton (attractive), the gravitophoton (two types, attractive

and repulsive), and the quintessence or vacuum particle

(repulsive), represented by hermetry forms H5, H11, and H12, see

Table 1. For additional features of hermetry forms see Tables 2-

conversion

7 Propulsion Concepts from Spacetime

Physics

In recent publications [9], [24] a gedankenexperiment was

developed to achieve the cancellation of the time T1 part in

the photon hermetry form in order to produce a gravitophoton.

Furthermore, in a very recent announcement by the European

Space Agency, 23 March 2006, the measurement of

an artificial gravitational field was reported, generated by a

rotating superconducting ring. In the following this experiment

will be analyzed in detail using the photon-gravitophoton

interaction, which is based on the possibility of

metric transformation. Second, a modified experiment is

suggested that should produce a force in the vertical direction

and thus might serve as the physical principle for a

field propulsion device.

7.1 Metric Transformation (Transmutation)

All physical interactions are mediated by so called messenger

particles (mediator particles) that are bosons. If each

physical interaction can be described by its individual metric

tensor, then the question arises: is it possible to cancel

metric terms in one hermetry form to obtain a different one.

This hermetry form then might represent a different physical

interaction. Looking at the hermetry forms for the photon

and the gravitophoton it seems, at least theoretically,

possible that the hermetry form of the photon is transformed

in the one of the gravitophoton. This means that an

interaction between electromagnetism and gravitation

should exist. Beside the details of the theoretical derivation,

the question of how to achieve such a conversion experimentally

is of prime importance. For this effect in order to

lead to a field propulsion principle, it must be understood

how the strength and the direction of the gravitational field

can be experimentally manipulated. Therefore, guidelines

need too be provided by theory that allow to design the

technical details needed for such a field propulsion device.

Although this effect, namely the coupling between electromagnetism

and gravitation, was predicted already in [24],

the recent experiment by Tajmar et al., see below, if proved

to be correct, would be a breakthrough, since an artificial

gravitational field would have been generated. Moreover,

the novel information obtained from this experiment with

regard to EHT is that there is a need to distinguish between

the coupling of fermions and bosons when gravitophotons

are to be generated. In previous publications the authors

only dealt with fermion coupling. As soon as the boson

coupling is taken into account, technical requirements such

as magnetic field strength seem to be substantially reduced

in comparison to fermion coupling.

7.1.1 Gravitomagnetic Field Experiment

In a recent experiment, funded by the European Space

Agency and the Air Force Office of Scientific Research,

Tajmar et al. [7] report on the generation of a toroidal (tangential,

azimuthal) gravitational field in a rotating accelerated

(time dependent angular velocity) superconducting Niobium

ring. In a recent presentation at Berkeley university

Tajmar [30] showed improved experimental results that

confirmed previous experimental findings.

This would be the first time that an artificial gravitational

field has been generated and, if correct, would have great

impact on future technology. Furthermore, the experiment

would demonstrate the conversion of electromagnetic interaction

into a gravitational field. This is exactly the effect

that is predicted by EHT, and both a qualitative and quantitative

explanation of this effect will be given below. Since

the experiment generates a tangential gravitational field, it

cannot be used directly as a propulsion system. It is, however,

of great importance, since it shows for the first time

that a gravitational field can be generated other than by the

accumulation of mass. In this section we will also discuss

the validity of the physical explanation, namely the Higgs

mechanism to be responsible for the graviton to gain mass,

given by Tajmar and de Matos [21], which they termed the

gyromagnetic London effect. According to these authors,

this effect is the physical cause for the existence of the

measured gravitational field.

The arguments of these authors are ingenious, but there is

some doubt whether the linearized Einstein equations, see

Eqs. (7, 8), can be used in the explanation of this effect, a

more detailed discussion is given in the next section.

In the following a derivation from first principles is presented,

using the fifth interaction from EHT, namely the

Heim-Lorentz force, but now using a coupling to bosons

(Cooper pairs) to explain this effect. Deriving this effect

from gravitophoton interaction, a physical interpretation

can be given that explains both qualitatively and quantitatively

the experimental results. Moreover, theoretical con11

Figure 7: In Heim space there are eight internal coordinates,

the four spacetime coordinates that are interpreted as energy

coordinates, since a length is associated with the R3 and T1 coordinates,

and four additional timelike coordinates (negative) signature,

giving rise to two additional subspaces S2 and I2. Hence,

Heim space H8 comprises four subspaces, namely R3, T1, S2, and

I2. The picture shows the complete set of metric-subspaces that

can be constructed from the polymetric tensor, Eq. 2. Each subspace

is denoted as hermetry form, which has a direct physical

meaning, see Table 2. In order to construct a hermetry form, either

internal space S2 or I2 coordinates must be present. In addition,

there are three degenerated hermetry forms, see Table 4

that are only partial forms of the photon and the quintessence

potential. They allow the conversion of photons into gravitophotons

as well as of gravitophotons and gravitons into quintessence

particles.

S2 S2 I2 I2

gik

3 T1

gik

g 12 ik

gik

3 T1

gik

4 gik

gik

3 T1

gik

Heim Space

In H8, there exists 12 subspaces, whose metric gives

6 fundamental interactions

(+ + + - - - - -)

signature of H8

siderations obtained from EHT lead to the conclusion that a

modified experiment will generate a gravitational field

acting parallel to the axis of rotation of the ring (torus),

see Fig.10, and thus can serve as a demonstrator for a field

propulsion principle 11. In this experimental configuration

the superconducting rotating ring is replaced by an insulating

disc and a set of superconducting coils as depicted, in

principle, in Fig. 10. The actual experiment configuration

would, however, be different. EHT allows to calculate the

magnitude and direction of the acceleration force and provides

guidelines for the construction of a propulsion device.

Although the experiment devised from EHT is different

from the one by Tajmar et al., the coupling to bosons is the

prevailing mechanism. According to the predictions of

EHT, experimental requirements, i.e., magnetic field

strength, current densities and number of turns of the solenoid,

are substantially lower than for fermion coupling

(vacuum polarization to change the coupling strength

via virtual pairs of electrons and positrons) that was so

far assumed in all our papers, see refs. [9], [13], [14], [24],

[29].

Materials for which a strong gravitational acceleration was

measured were niobium (Nb, TC = 9.4 K) and lead (Pb, TC

= 7.2 K). No gravitational field was measured in YBCO

(Yttrium barium copper oxide, YBa2Cu3O7-x, TC = 94 K)

and BSCCO ( Bismuth strontium calcium copper oxide,

Bi2Sr2CanCun+1O2n+6, TC = 107 K) which are so called high-

11 A detailed discussion will be given in our forthcoming paper entitled

Artificial Gravitational Fields.

temperature superconductors whose critical current density

is substantially lower than that for Nb or Pb. The effect is

strongest in Nb which can sustain a magnetic induction of

up to 20 Tesla. In the next section, a theoretical derivation

of the gravitomagnetic field strength is given, based on

gravitophoton interaction, which is the interaction between

electromagnetism and gravitation predicted by EHT.

At critical temperature TC some materials become superconductors

that is, their resistance goes to zero. Superconductors

have an energy gap of approximately Egap  3.5

kTC. This energy gap separates superconducting electrons

below from normal electrons above the gap. At temperatures

below TC , electrons are coupled in pairs, called Cooper

pairs, which are bosons. The exact formation of Cooper

pairs is not known. The coupling of the electron pairs

seems to be via phonons, generated by electron movement

through the lattice of the superconductor. The size of a

Cooper pair is some 103 nm. The crystal lattice contains defects

that lead to an energy transfer E from the electron

gas to the lattice. E must be smaller than Egap , otherwise

the Cooper pairs are destroyed.

The speed of the Cooper pairs can be calculated in a coordinate

system where the electron gas is at rest and the lattice

is moving, applying classical energy and momentum conservation.

Decelerating the grid means that Cooper pairs

gain energy. The maximum amount of energy that a Cooper

pair can absorb is Egap , otherwise it is lifted in the band

above, and superconductivity is lost. Therefore the simple

ansatz

mvc

2=Egap=3.5k TC

(6)

can be used, vc denoting the velocity of a Cooper pair. At

temperature TC = 10 K a speed of about vc = 104 m/s is obtained.

A smaller band gap therefore cause a decrease in the

speed of the Cooper pairs. Quantum mechanics calculations

yield a more correct value of some vc = 105 m/s.

7.1.2 Artificial Gravity Experiment Explained by

Gravitophoton Interaction

Considering the Einstein-Maxwell formulation of linearized

gravity, a remarkable similarity to the mathematical

form of the electromagnetic Maxwell equations can be

found. In analogy to electromagnetism there exist a gravitational

scalar and vector potential, denoted by g and Ag, respectively

[7]. Introducing the corresponding gravitoelectric

and gravitomagnetic fields

e :=−∇gand b:=∇×Ag (7)

the linearized version of Einstein's equations of GR can be

cast in mathematical form similar to the Maxwell equations

of electrodynamics, the so called gravitational Maxwell

equations, Eqs. (8)

Figure 8: The picture shows the ratio of temperature over critical

temperature versus the ratio of energy gap over energy gap at 0

Kelvin. Since the specific heat close to 0 Kelvin is low, small

amounts of energy will result in drastic temperature increase, the

height of the energy gap is substantially impacted and thus the velocity

of the Cooper pairs. The temperature must stay below T/Tc <

0.3 to guarantee the maximal velocity of the Cooper pairs.

BCS curve

Tin

Tantalum

Niobium

T/Tc

Eg(T)/Eg(0)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

∇⋅e=−4G ,∇⋅b=0

∇×e=0 ,∇×b=−

16G

c2 j

(8)

where j= v is the mass flux and G is the gravitational

constant12. The field e describes the gravitational field form

a stationary mass distribution, whereas b describes an extra

gravitational field produced by moving masses.

Fig. 9 depicts the experiment of Tajmar et al., where a superconducting

ring is subject to angular acceleration, which

should lead to a gravitophoton force. EHT makes the following

predictions for the measured gravitational fields

that are attributed to photon- gravitophoton interaction, the

fifth interaction.

• For the actual experiment pictured in Fig. 9, the

gravitophoton force is in the azimuthal direction

only (Tajmar et al.) caused by angular acceleration

of the superconducting niobium disk. The acceleration

field is opposite to the angular acceleration,

obeying some kind of Lenz rule.

• For the gedankenexperiment of Fig. (10), a force

component in the vertical direction would be

generated.

It will be shown in the following that the postulated gravitophoton

force completely explains all experimental facts

of Tajmar's experiment, both qualitatively and quantitatively.

It is well known experimentally that a rotating superconductor

generates a magnetic induction field, the so called

London moment13

B=−

2me

 (9)

where ω is the angular velocity of the rotating ring. It

should be noted that the magnetic field in Tajmar' s experiment

is produced by the rotation of the ring, and not by a

current of Cooper pairs that are moving within the ring.

It should be remarked that there is a major difference between

the experiment of Fig. 9 and the proposed experiment

depicted in Fig. 10, which is in the generation of the

magnetic induction field B.

De Matos and Tajmar [31] postulate a gravitomagnetic

London moment as explanation for the observed acceleration

field. This means that in analogy to the London equations

and along with the concept of spontaneous symmetry

breaking a Klein-Gordon type equation for particles of any

type of spin (also called Proca equation for spin 1 particles)

can be formulated.

12 Here no consideration is given to the fact that G comprises three

parts according to EHT, see Fig. 6.

13 The mass and charge of the Cooper pairs needs to be used.

In superconductivity spontaneous symmetry breaking (below

the critical temperature TC , two electrons may be coupled

by phonons, forming so called Cooper pairs, i.e.,

breaking the random behavior of the electron gas in the

crystal and generating the collective phenomenon of superconductivity)

occurs at very low temperatures being responsible

for the Meissner effect. This means that the magnetic

field lines cannot penetrate into the medium and remain

in a thin layer on the surface, in which the magnetic

field strength falls of exponentially. Hence, there is a finite

range electromagnetic field, which corresponds to a massive

photon [17]. The penetration depth of the field is associated

with the wavelength of the photon and, using its respective

Compton wave length, the mass of the photon

within the superconductor can be determined. It should be

noted, however, that the Proca equations for the photon

and the graviton are basically different, since the photon

has spin 1 and therefore the wave function is a four vector

(four potential Am), while the graviton has spin 2, and the

wave function is a tensor of rank 2. If, however, the linearized

Einstein equations are used, Eqs. 7, 8, there exists a direct

analogy with regard to the electromagnetic Proca equations.

The argument is that the gravitational field is weak

and therefore this approach should be justified. There remains

the fact that the linearized equations are used to calculate

an effect which is 31 orders of magnitude higher

than originally predicted by these equations. The phenomenological

consequences of mass accumulation of the photon

due to the Higgs mechanism leads to the Proca equation

(or second London equation) for the photon. Assuming a

gravitomagnetic analogy requires that the Higgs mechanism

(massless particles obtain mass through the all pervading

scalar Higgs field) would also be responsible for the

mass accumulation of the graviton. The action of the Higgs

field was deliberately designed so as to generate spontane13

Figure 9: Rotating superconducting torus (Niobium) modified

from Tajmar et al., see ref. [7]. All dimensions are in mm. A cylindrical

coordinate system (r, θ, z) with origin at the center of the

ring is used. In Ring accelerometers measure a gravitational acceleration

of some 100 μg in the azimuthal (tangential, θ) direction

when the ring was subject to angular acceleration, ˙ . The acceleration

field does not depend on ω. No acceleration was measured

in the z-direction (upward). A more recent experiment employed

a set of 4 in-ring accelerometers and confirmed the rotational

character of this field. If the direction of rotation is reversed,

the acceleration field changes sign, too.

ez

er

e

ous symmetry breaking for electroweak interactions.

However, the current Standard Model of high-energy physics

is definitely not applicable to gravitation. There also

exists a difference between the massive photon and the

massive graviton. The massless photon and graviton both

only possess two states of polarization. The difference occurs,

however, when they become a massive photon (three

polarization states) and a massive graviton (five polarization

states). De Matos and Tajmar now postulate that the

observed acceleration field bg, produced by the rotating superconductor,

is equivalent to an additional magnetic field

B that has to be added to the magnetic field of the London

moment, see Eq. (9). This alludes to postulating that a nonrelativistic

particle of velocity v with charge q and mass m

has the Lagrangian L=½mv2−q v⋅A−m v⋅Ag where

A is the electromagnetic vector potential and Ag denotes the

gravitational vector potential of Eq. (7). However, postulating

that gravitation is analogous to electrodynamics causes

a contradiction, since the photon has spin 1 and thus is described

by three independent fields, namely the spinvector

in space. Thus the components of A are not independent

and must satisfy ∂ A=0. On the other hand, as was

said above, a massive graviton has five polarization states

and cannot be described by a four vector.

However, this seems to require a fairly strong coupling, between

electromagnetics and gravitation by a factor me /e.

This needs to be postulated also, since the four known

physical forces do not provide such a direct coupling. Last

but not least, if quantum corrections are added to the Higgs

boson mass at the grand unification scale (1015-1016 GeV),

the Higgs mass becomes huge. Although this is not the energy

level at which the experiment operates, it shows that

something is not right with the Higgs mechanism itself

[32]. De Matos and Tajmar, however, do not use the Higgs

field mechanism to calculate the mass gained by the graviton

inside the superconductor, but directly use the measured

mass values of the Cooper pairs [31].

On the other hand, a coupling between electromagnetism

and gravitation is a basic fact of EHT, because of the fifth

fundamental interaction, which foresees a conversion of

hermetry form H7, describing the photon, into the hermetry

form H5, describing the gravitophoton, compare Table 2. In

the following, results from EHT are used to explain the

source and to calculate the magnitude of the measured acceleration

field.

The experiment shows that the acceleration field vanishes if

the Cooper pairs are destroyed. This happens when the

magnetic induction exceeds the critical value BC(T), Fig.

8, which is the maximal magnetic induction that can be sustained

at temperature T, and therefore dependents on the

material. The rotating ring is no longer a superconductor

and the acceleration field vanishes. Eq. 10 assumes that the

system is in superconducting state and sufficient Cooper

pair density exists.

In the official version (termed short version) of this paper a

factor B/Bmax was introduced into Eq. 10. However, in a recent

conversation with M. Tajmar (July 2006), we learned

that the measuring process of the acceleration does not take

place at a specified angular velocity w, as we had assumed

previously. This factor was added by us to model a putative

w dependency of the acceleration field, and could not be

obtained from EHT. As was pointed out by Tajmar, instead,

the superconductor is rotated with constant or variable angular

acceleration, from angular frequency 0 up to a maximum

value. The measured data show no dependence on w,

and thus this factor is not at all needed. Therefore, the original

derivation as obtained by EHT is used in the following

analysis without insertion of any additional parameters.

EHT predicts that the magnetic induction field B is equivalent

to a gravitophoton (gravitational) field bgp. The following

relation is utilized, derived from EHT but stated here

without proof

bgp∝

B (10)

where me and mp are the electron and proton mass. The

neutral gravitophoton decays in a gravitationally attractive

(negative) and a gravitationally repulsive gravitophoton.

The negative one interacts with the electron and the repulsive

one interacts with the proton14. From EHT the following

general relationship between a magnetic and the neutral

gravitophoton field, bgp, can be derived

bgp= 1

1−k1−ka

−1 em

B (11)

where k = 1/24 and a = 1/8. It should be noted that values

of coupling constants k and a were derived some ten years

ago, and are published in [33], see Eq. (11) p. 64, Eq. (15)

p. 74, and Eq. (16)15 p. 77. No parameter was adjusted in

the derivation of Eq. 16. At present the dependency of coupling

constants k and a on the Cooper pair density was not

considered. The values used are accurate for niobium but

would be different for lead.

Moreover, the theory also correctly predicts direction and

sign of the acceleration field. This is seen as a sign that the

predicted six fundamental interactions may actually exist in

Nature.

The dimension of bgp of is s-1. Differentiating Eq. 11 with

respect to time, results in

∂ bgp

∂t

= 1

1−k 1−ka

−1 e

∂ B

∂t . (12)

Integrating over an arbitrary area A and using the gravitational

induction equation yields

15 It should be noted that the quantity w3

2 used in this ref. is

termed w ph _ gp

2 in our terminology, see also EHT glossary at

www.hpcc-space.com.

∫ ∂bgp

∂t

⋅d A=∮e gp⋅d s=∮ ggp⋅d s (13)

where it was assumed that the gravitophoton field, subscript

gp, since it is a gravitational field, see Fig. 6, is separated

according to Eqs. (7, 8). As the above formulas will

be applied to the experimental configurations depicted in

Figs. 9 and 10, cylindrical coordinates r, θ, z are employed.

ggp is the acceleration field generated by the gravitophoton

field. Combining Eqs. 12 and 13 gives the following relationship

∮ ggp⋅d s= 1

1−k 1−ka

−1 e

∫ ∂ B

∂ t

⋅d A (14)

From Eq. 9 one obtains

∂ B

∂t

=−

2me

e ˙ . (15)

Next, we apply Eqs. 14 and 15 to the experimental configuration

of Fig. 9, calculating the gravitophoton acceleration

for the in-ring accelerometer. It is assumed that the accelerometer

is located at distance r from the origin of the

coordinate system. From Eq. 9 it can be directly seen that

the magnetic induction has a z-component only. Applying

Stokes law to Eq. 14 it is clear that the gravitophoton acceleration

is in the r-θ plane. Because of symmetry reasons the

gravitophoton acceleration is independent on the azimuthal

angle θ, and thus only has a component in the circumferential

(tangential) direction, denoted by e . Since the gravitophoton

acceleration is constant along a circle with radius

r, integration is over the area A=r2 ez . Inserting Eq.

15 into Eq. 14, using the standard values for k and a (in a

forthcoming paper their dependency on the superconductor

material will be shown), and carrying out the integration,

the following expression for the gravitophoton acceleration

is eventually obtained

ggp=−0.04894

˙ r (16)

where it was assumed that the B field is homogeneous over

the integration area. Now the experimental values taken

from the paper by Tajmar et al. [7] will be inserted. The following

values were used:

˙ =103rad /s2 ,r=3.6×10−2m ,me /mp=1/1836

The angular acceleration was determined from the slope fit

of Fig. 6 in ref. [7] and the r value was determined from

Fig. 9. Inserting the proper values into Eq. 16 finally delivers

the theoretical value of the gravitophoton acceleration

for the experiment by Tajmar et al.

ggp=−0.04894×5.447×10−4×3.6×10−2×103×9.81−1 g (17)

resulting in the final value for the circumferential acceleration

field

ggp=−0.978×10−4 g . (18)

From Fig. 6 in ref. [7] an experimental value of about

1.0×10-4 g was determined. For a more accurate comparison,

the coupling factor kgp for the in-ring accelerometer, as

defined by Tajmar, is calculated from the value of Eq. 18,

resulting in kgp = -9.78´10-8s2. The measured values is kgp =

-7.64 ± 0.28´10-8s2. This means that the theoretical value is

still within measuring tolerance. Thus there is a close

agreement between the predicted gravitophoton force and

the measured acceleration. It should be kept in mind that

the present derivation does not lead to a dependence on the

density of Cooper pairs, but it can be shown that the coupling

values k and a depend on this density. Considering

both the mathematical and physical complexity of the derivation

the closeness of theory and experiment is remarkable.

In a forthcoming paper the differences for niobium

and lead will be explained.

7.1.3 Gravitomagnetic Field Propulsion by

Gravitophoton Interaction

The experiment by Tajmar et al. generates an azimuthal

gravitational field, and thus is not suitable for propulsion.

The lesson learned from the experiment by Tajmar et al. is

that the coupling to bosons (Cooper pairs) is of prime importance.

However, the structure of the Heim-Lorentz force

equations remains unchanged for boson coupling. Employing

the Heim-Lorentz force equations to the experimental

setup of Fig. 10, Heim-Lorentz force now produces two

force components: one in the radial r direction, and the

second one in the z- direction. These components are given

Fr  er=me v

T bz e×ez (19)

Fz ez=

v

mn v

T bz e×ez ×e (20)

where v

T denotes the velocity of the rotating disk or

ring, and bz is the component of the (gravitational) gravitophoton

field bgp in the z-direction. In contrast to the fermion

coupling, ref. [24], experimental requirements seem to be

modest.

The superconducting current loop (blue), see Fig. 10, provides

an inhomogeneous magnetic field at the location of

the rotating disk (red). The z-component of the gravitophoton

field, bz is responsible for the gravitational field above

the disk. This experimental setup also serves as the field

propulsion device, if appropriately dimensioned. Moreover,

using EHT, a gedankenexperiment can be devised that produces

a gravitational force in the direction of the axis of

rotation. Fig. 10 describes the experimental setup for

which an insulating disk rotates above a superconducting

solenoid. The material would not be niobium.

In the gedankenexperiment of Fig. 10, the gravitophoton

force produces a gravitational force above the disk in the zdirection

upward and also in the radial direction. It

should be noted that the actual experiment would be different.

The velocity of the Cooper pairs with regard to the lab

system is given by rω in the gedankenexperiment of Fig.

10. The actual velocity of the Cooper pairs can be determined

from Fig. 10.

The following assumptions were made: N = 100, number of

turns of the solenoid; current of some 1-2 A (needed to calculate

bz); diameter of solenoid 0.1 m; and v

T=10m/s .

A detailed analysis predicts an acceleration in z-direction of

some 4.0×10-4 g. From these numbers it seems to be possible

that, if our theoretical predictions are correct, the realization

of a workable space propulsion device that can

lift itself from the surface of the earth seems to be feasible

with current technology.

Conclusions and Perspectives

In this paper an overview of the current status of space propulsion

was given. It has been shown that even with an advanced

fission propulsion system (the only device that

might be feasible among the advanced concepts within the

next several decades), space travel will be both very limited

regarding, speed, range, and payload capability as well as

extremely costly. Travel time to other planets will remain

prohibitively high. One can safely forget interstellar

travel.To fundamentally overcome these limitations, physical

laws hitherto not known are needed. If current physics

would be the final answer, mankind would clearly be restricted

to the solar system. Therefore, the search for novel

physics is justified, because of the potential extreme benefits.

GR is based on the concept of continuous spacetime provided

with a metric. Metric engineering of spacetime or using

wormholes (singularities) will allow, at least in principle,

to overcome some of the limitations, but requires additional

concepts such as negative energy density that have

not been found in Nature. The whole concept does not

seem to be technically feasible.

On the other hand, the recent experiment by Tajmar, if confirmed,

has shown some evidence that a coupling between

electromagnetism and gravitation might exist, which would

allow the generation of artificial gravitational fields. Extended

Heim Theory has predicted this effect, and was used

to successfully describe and to quantitatively calculate this

experiment. In addition, EHT also allows to devise a gedankenexperiment

that produces a gravitational field along the

axis of rotation of a rotating ring that is self-propelled, and

thus can be used to build a propellantless propulsion device.

Superconductivity with a high density of Cooper pairs (collective

phenomena) is essential for the coupling between

electromagnetism and gravitation.

EHT belongs to a well known class of gauge theories. The

novel features of the theory are in the introduction of an internal,

factored 8-dimensional space to describing the additional

fundamental symmetries. A novel feature is the construction

of a polymetric tensor which comprises all possible

physical interactions. The coupling constants of the interactions

were obtained from number theory considerations,

and thus are calculated.

The type of coupling that seems to occur in the experiment

by Tajmar et al. is included in EHT, which knows six fundamental

physical interactions. The two additional forces

are gravitation like, but gravitation can be both attractive

and repulsive. The guidelines provided by the theory can be

used for a demonstration experiment of a field propulsion

device, which would not require substantially higher

experimental effort than the original experiment. Research

therefore should focus on the modified experiment, because

of its substantial applications in the field of transportation

as well as on the theoretical foundations of physical interactions.

Perhaps the sixth interaction, represented by the

quintessence particle, could provide a theoretical explanation

for the measured value of the cosmological constant.

In a forthcoming paper, the dependence on the coupling

constants on the superconductor material will be reported.

ACKNOWLEDGMENT

The authors are most grateful to Prof. P. Dr. Dr. A.

Resch, director of the Institut für Grenzgebiete der Wissenschaft

(IGW), Innsbruck, Austria for his continuous support

and hospitality in writing this paper.

 

ez

er

e

Figure 10: The picture shows the physical principle of the experimental

setup to generate a gravitational field in the z-direction

(upward, above rotating disk) by the Heim-Lorentz force

using a superconducting coil (boson coupling) and a rotating

disk or ring. The actual experiment would be different.

The authors are particularly grateful to Dr. M. Tajmar,

ARC Seibersdorf, Austria for clarification of the measuring

process of the acceleration field in his recent experiment

that lead to a revision of our calculations.

We are also grateful to Prof. P. Papadopoulos, San Jose

State University, CA, Prof. T. Waldeer, TU Claustahl and

Univ. of Applied Sciences, Salzgitter as well as Dr. A. Müller

for correcting parts of the manuscript.

The second author was partly funded by Arbeitsgruppe Innovative

Projekte (AGIP) and by Efre (EU) at the Ministry

of Science and Education, Hannover, Germany.

Special thanks go to our friends at the bed and breakfast

Adella Villa, Atherton, CA for their hospitality where part

of this paper was written by the second author.

References

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Press, 2005.

2. Zaehringer, A.: Rocket Science, Apogee Books, Chap.

7, 2004.

3. Mallove, E. and G. Matloff, The Starflight Handbook,

Wiley, Chap. 3, 1989.

4. Jahnshan, S.N., and T. Kammash: Multimegawatt Nuclear

Reactor Design for Plasma Propulsion Systems,

Vol 21, Number 3, May-June 2005, pp.385-391.

5. Emrich, W.J. And C.W. Hawk: Magnetohydrodynamic

Instabilities in a Simple Gasdynamic Mirror Propulsion

System, Vol 21, Number 3, May-June 2005, pp.

401-407.

6. Czysz, P., Bruno, C: Future Spacecraft Propulsion Systems,

Springer, 2006.

7. Tajmar, M. et al.: Experimental Detection of the Gra-vitomagnetic

London Moment, arXiv, gr-qc/

06030332006.

8. Wesson, P. S., Five-Dimensional Physics, World Scientific,

2006.

9. Dröscher, W., J. Hauser, Heim Quantum Theory for

Space Propulsion Physics, AIP, STAIF, 2005.

10.Krauss, L.M., Propellantless Propulsion: The Most Inefficient

Way to Fly?, NASA/CP 208694, January 1999.

11. Rovelli, C.: Loop Quantum Gravity, IoP, November

2003.

12.Altland, A., B. Simons: Condensed Matter Field Theory,

Cambridge Univ. Press, 2006.

13.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.

14.Dröscher, W., J. Hauser: Magnet Experiment to Measuring

Space Propulsion Heim-Lorentz Force, AIAA

2005-4321, 42nd AIAA/ASME/SAE/ASE, Joint Propulsion

Conference & Exhibit, Tuscon, Arizona, FL, 10-13

July, 2005.

15. Liddle, A.: An Introduction to Modern Cosmology, Wiley,

2003.

16. Witten, E: Reflection on the Fate of Spacetime, Physics

Today, 1996.

17.Kaku, M.: Quantum Field Theory, Chap. 19, Oxford,

1993.

18. Levin, J.: How the Universe Got its Spots, Penguin

Press, 2003.

19.Hartle, J. B.: Gravity, Addison Wesley, 2003.

20.Vass, R..: Tunnel durch Raum und Zeit, Kosmos, Stuttgart,

2005.

21. de Matos, C. J., Tajmar, M.: Gravitomagnetic London

Moment, and the Graviton Mass Inside a Superconductor,

PHYSICA C 432, 2005, pp.167-172.

22. Zwiebach, R., Introduction to String Theory, Cambridge

Univ. Press, 2004.

23.Greiner, W., Müller, B.: Quantum Mechanics Symmetries,

Springer, 1994.

24.Dröscher, W., J. Häuser: Physical Principles of Advanced

Space Transportation based on Heim's Field

Theory, AIAA/ASME/SAE/ASE, 38th Joint Propulsion

Conference & Exhibit, Indianapolis, Indiana, 7-

10 July, 2002, AIAA 2002-2094, 21 pp.

25. Schiller, C.: Motion Mountain, The Adventure of Physics

(Chap. XI), September 2005,

www.motionmountain.net.

26.Heim, B.: Vorschlag eines Weges einer einheitlichen

Beschreibung der Elementarteilchen, Zeitschrift für

Naturforschung, 32a, 1977, pp. 233-243.

27.Heim, B.: Elementarstrukturen der Materie, Band 1, 3.

Auflage, Resch Verlag, Innsbruck, 1998.

28.Anderson, P.W., Science 177 (1972), pp. 393-396.

29.Dröscher, W., J. Häuser: Future Space Propulsion

Based on Heim's Field Theory, AIAA 2003-4990,

AIAA/ASME /SAE/ASE, Joint Propulsion Conference

& Exhibit, Huntsville, AL, 21-24 July, 2003, 25 pp.

30. Tajmar, M.: private communnication, 13 July 2006.

31. de Matos, C.J., Tajmar, M.: Gravitomagnetic London

Moment and the Graviton Mass Inside a Superconductor,

PHYSICA C 432, 2005, pp. 167-172.

32. Bergström, L, A. Goobar: Cosmology and Particle Astrophysics,

Springer,2004.

33.Heim, B. and Dröscher, W.: Strukturen der Physikalischen

Welt und ihrer nichtmateriellen Seite, Resch Verlag,

Innsbruck, 1996.

Table 2: Table of hermetry forms describing the six fundamental interaction particles (interaction fields): classification

scheme for physical interactions and particles (for hermetry forms not shown see Table 3) obtained from polymetry in Heim space

H8. Superscripts for subspaces indicate dimension. Subspaces S2 and I2 stand for organization and information, respectively. A hermetry

form characterizes either a physical interaction, a particle or a class of particles (see Table 3), and is associated with an admissible

subspace (a space that has a real physical meaning) of H8 , which is a combination from the four elementary subspaces

comprising H8. Any admissable subspace either needs S2 or I2 or both types of coordinates to be present in order to realize physical

events in our spacetime. Elementary subspaces R3, T1, S2 and I2 form the basis of Heim space H8. Employing this selection rule

leads to 12 admissible hermetry forms, Fig 7. The additional four dimensions of the original space H12 are not needed for describing

physical interactions, but seem to steer probability amplitudes and are not of interest here. It should be noted that a white field

in a table entry of the messenger particle column implies that the corresponding hermetry form does not describe an interaction

particle and is therefore listed separately in Table 3. The six different colors in the messenger particle column indicate the six fundamental

interactions.

Subspace Hermetry form

Lagrange density

Messenger particle Symmetry

group

Physical interaction

S2 H1S2 , LG

graviton U(1) gravitation +

S 2×R3 H2S 2×R3

S 2×T 1 H3S2×T1

S 2×R3×T 1 

particle aspect

H4 S2×R3×T 1

S 2×I 2 H5S2×I 2 , Lgp − neutral

three types of

gravitophotons

U(1)´U(1) gravitation ±

+ attractive -

repulsive

S 2×I 2×R3 H6 S2×I 2×R3 , Lew Z0

boson

SU(2) weak

S 2×I 2×T1 H7S2×I 2×T 1 , Lem

photon U(1) electromagnetic

S 2×I 2×R3×T1 H8 S2×I 2×R3×T 1 W ± bosons SU(2) weak

wave

aspect { I 2

I 2×R3

I 2×T1

I 2×R3×T 1} H9 I 2 , Lq

quintessence U(1) gravitation -

vacuum

H10  I 2×R3 , Ls

gluons SU(3) strong

H11 I 2×T1

H12  I 2×R3×T 1

Table 1: The three gravitational interactions are related to different types of matter as indicated in the first column. The gravitational

hermetry forms are explained in Tables 2 and 3.

Generated by Messenger particles Force Coupling constant Hermetry form

real particles graviton attractive Gg H1 S 2

virtual particles gravitophoton repulsive and attractive

Ggp

+ ,Ggp

- =1/672Gg H5 S 2×I2 

Planck mass vacuum

quintessence or

vacuum particle

repulsive Gq=4.3565×10-18 Gg H9 I2 

Table 3: Table of real particles and their interactions. The lepton weak charge is responsible for the following interactions:

lepton weak charge for interactions of: e and ne, m and nm , t and nt as well as interactions between neutrinos caused by Z 0 and

W ± bosons.

Subspace Hermetry form Particle class

S 2×T 1 H3S2×T1 weak charge for leptons

S 2×R3×T 1 H4 S2×R3×T 1 electrically charged particles

S 2×R3 H2S 2×R3 neutral particles with rest mass

I 2×T1 H11 I 2×T1 weak charge for quarks

I 2×R3×T 1 H12  I 2×R3×T 1 quarks

Table 4: Table of the three degenerated hermetry forms: A * indicates that the metric tensor is from the associated space, but

some of the fundamental metric components of that space are 0, which is denoted as degeneration. In the first row the probability

amplitude for the conversion of photons into gravitophotons is shown. The third row shows the conversion amplitude from gravitophpotons

into the quintessence particle.

Subspace Associated space Physical quantity Metric tensor

R3 H13*T1×S2×I 2 wph _ gp

G = (44, 55, 56, 57, 58

65, 75, 85,

66, 67, 68,

76, 77, 78,

86, 87, 88)

H14 * R3×S 2 neutrinos

H15* I 2 wgp _q

G = (77, 88)

T 1

R3×T 1

AIAA2006-4608LetterExtndVersionRevisedSept.pdf (5,1 MB)

SPACETIME PHYSICS AND ADVANCED PROPULSION CONCEPTS Short Version

02.05.2014 18:23

AIAA2006-4608LetterShortVersion.pdf (5 MB)

AIAA 2006-4608

SPACETIME PHYSICS AND

ADVANCED PROPULSION CONCEPTS

Walter Dröscher1, Jochem Hauser1,2

1Institut für Grenzgebiete der Wissenschaft, Innsbruck, Austria

and

2Faculty Karl-Scharfenberg, University of Applied Sciences, Salzgitter, Germany

Short Version

Abstract: Spacetime physics includes general relativity (GR), quantum theory, quantum gravity, string theory (additional external

dimensions), and gauge theory (additional internal dimensions) as well as some modern variations. The paper will discuss

the requirements on future propulsion systems stemming from the demands for routine missions to LEO, the moon, or

planetary missions within the solar system, as well as interstellar flight. These requirements are compared with the limits imposed

by the physical laws of GR in conjunction with the physical theories listed above. The physical consequences of these

field theories in curved-spacetime as well as string and gauge theory, are discussed. Moreover, recent developments in the

structure of spacetime are presented, and their consequences for advanced propulsion systems are outlined. In particular, a

novel experiment (ESA, March 2006) reporting about the generation of an artificial gravitational field in the laboratory is discussed.

This experiment, if confirmed, could serve as the basis for a field propulsion device. Since a thorough understanding

of the underlying physical principle is of prevailing importance, a detailed theoretical analysis of this experiment is presented.

Utilizing the experimental data along with the insight gained from theoretical considerations, a concept for a field propulsion

device is developed. Preliminary results on the capability of this device will be given. Finally, an outlook of the necessary experimental

and theoretical prerequisites is given to both understand the novel physics as well as the technical requirements for

such a propulsion device.

1 Senior scientist, 2 Senior member AIAA, member SSE, © IGW, Innsbruck, Austria 2006

 

ez

er

e

1 Spacetime and Space Propulsion2

Space flight within the solar system requires the covering

of large distances. The distance to our moon is some

3.8×105 km, while Mars, our favorite destination is some

0.5 A.U. away (astronomical units, 1 A.U. = 1.5×108 km).

The next planet, Jupiter, is already some 4 A.U. away

from Earth. The closest star is Proxima centauri, which is

1.30 pc away from earth (parsec, 1pc = 3.3 ly) or, using

lightyear, the distance light travels in the time of 1 year,

(1 ly = 9.46×1012 km), it would take the light some 4.3

years to reach this star. Expressed in miles, the distance is

some 25 trillion miles from earth. The star closest to us

which is similar to our sun with respect to size and surface

temperature is Centauri, some 1.33 pc away. But

these distances are small when compared to the dimension

of the Milky Way Galaxy which comprises a galactic

disk of some 100,000 ly in diameter and some 4,000 ly

for the galactic bulge. Our solar system is located some 8

kpc (kilo parsec) from the galactic center. Our galaxy

contains some 100 billion stars, and the universe contains

some 100 billion galaxies. The farthest of these galaxies

is some 13 billion ly away, which is roughly the size of

the observable universe. The age of the Earth is estimated

to be some 4.5 billion years, while there are stars that are

7 to 10 billion years old. Having mentioned both distance

and time, the concept of spacetime has been utilized and

also, implicitly, the concept of metric has been employed

to measure distances in this four-dimensional spacetime.

This is the environment in which spaceflight has to take

place.

Next, we will briefly discuss our current capabilities 3 to

travel through space and time that is, in spacetime. Current

space transportation systems are based on the principle

of momentum generation, regardless whether they are

chemical, electric, plasma-dynamic, nuclear (fission) or

fusion, antimatter, photonic propulsion (relativistic) and

photon driven (solar) sails, or exotic Bussard fusion ramjets,

solar sails, nuclear explosions (pusher, Orion), antimatter

propulsion are most likely in the realm of unfeasible

technologies because of the large engineering and/or

safety problems as well as their prohibitively high cost.

The specific impulse achievable from thermal systems

ranges from some 500 s for advanced chemical propellants

(excluding free radicals or metastable atoms), some

2 Invited paper in the session 50-NFF-3 Faster Than Light, AIAA 42nd

Joint Propulsion Conference, Sacramento, CA, 9-12 July 2006. A

more detailed paper will be available at the conference.

3 The cover picture shows a combination of two pictures. The first one,

taken from ref. [1], shows a view (artist's impression) from an existing

planet orbiting the solar-type star HD 222582 some 137 ly away.

The second one depicts the principle of the propulsion system used to

reach this planet, see Fig. 3.

1,000 s for a fission solid-core rocket (NERVA program

[2]) using hydrogen as propellant (for a gas-core nuclear

rocket specific impulse could be 3,000 s or higher but requiring

very high pressures) up to 200,000 s for a fusion

rocket [3]. Although recently progress was reported in the

design of nuclear reactors for plasma propulsion systems

[4] such a multimegawatt reactor has a mass of some

3×106 kg and, despite high specific impulse, has a low

thrust to mass ratio, and thus is most likely not capable of

lifting a vehicle from the surface of the earth. With regard

to fusion propulsion, the gasdynamic mirror has been proposed

as highly efficient fusion rocket engine. However,

recent experiments revealed magneto-hydrodynamic instabilities

[5] that make such a system questionable even

from a physics standpoint, since magnetohydrodynamic

stability has been the key issue in fusion for decades. The

momentum principle combined with the usage of fuel, because

of its inherent physical limitations, will not allow

going to routine spaceflight. The above discussion does

not even consider the difficulties entered when the simplicity

of the physical concept meets the complexities of

the workable propulsion system.

At relativistic speeds, Lorentz transformation replaces

Galilei transformation that is, the rest mass of the propellant

is multiplied by the factor (1 - v2/c2) that goes to infinity

if the exhaust velocity v equals c, the speed of light

in vacuum.

For instance, a flight to the nearest star at a velocity of

some 16 km/s would take about 80,000 years. If the speed

of light cannot be transcended, interstellar travel is impossible.

We conclude with a phrase from the recent book on

future propulsion by Czysz and Bruno [6] : If that remains

the case, we are trapped within the environs of the

Solar System. In addition, the current state of propulsion

does not allow either convenient interplanetary travel and

inflicts prohibitively high cost even for low earth orbits.

As mentioned by Krauss [7], general relativity (GR) allows

metric engineering, including the so-called warp

drive, see Sec. 2.2, but superluminal travel would require

negative energy densities. Furthermore, in order to tell

space to contract (warp), a signal is necessary that, in

turn, can travel only with the speed of light. GR therefore

does not allow this kind of travel.

On the other hand, current physics is far from providing

final answers. First, there is no unified theory that combines

GR and QM (quantum mechanics). Second, not

even the question about the total number of fundamental

interactions can be answered. Hence, the goal to find a

unified field theory is a viable undertaking, because it

might lead to novel physics, which, in turn, might allow

for a totally different principle in space transportation.4

2 Classical Spacetime

In GR the model of space and time supports continuous

and differentiable functions and provides a structure that

has the same local topology as ℝ4. Therefore, spacetime is

a topological space and thus comprises a collection of

open sets. For small regions it is assumed that the open

sets possess the topology of ℝ4. Therefore, a one-to-one

mapping exists between the open set of spacetime and ℝ4.

Each point in spacetime has a unique image in ℝ4 and vice

versa.

2.1 Spacetime as a Manifold

Equipped with the features described above, spacetime is

called a manifold. In general, physical fields defined on

an open set of this manifold are assumed to be differentiable.

Spacetime thus is considered to be a multiply differentiable

manifold. However, as will be shown in Sec. 3,

spacetime must be quantized. Therefore, it is not generally

possible to have a third point between any two points

in spacetime. Spacetime is not dense and hence the concept

of manifold is incorrect, at least on the Planck

length, see below. In SRT (special theory of relativity)

Lorentz contraction is continuous, but this contradicts the

concept of minimum length.

At Planck scales SRT cannot be correct. GR uses the concept

of curvature, but at Planck scales it cannot be measured

exactly. This is equivalent to fluctuations of curvature

and thus of gravitation itself. A unified field theory

describing all physical interactions by individual metrics

would be subject to fluctuations as well that is, all physical

forces would be subject to these fluctuations.

Physics is not possible below the Planck scale, since concepts

of metric, dimensionality, or points are not defined.

Spacetime itself is a field and thus needs to be quantized,

leading to quantum gravity (QG), see, for instance [8]. So

far, QG has not lead to a unified field theory, and does not

predict phenomena that could lead to a novel propulsion

concept. Conventional wisdom claims that quantized spacetime

acts on the Planck scale only. On macroscopic

scales the concepts of GR are sufficient to describe spacetime.

However, this argument may turn out to be invalid,

since despite the smallness of the quantized action, denoted

by the Planck constant ℏ, physical phenomena on the

macroscopic scale do occur, for instance superconducting.

Therefore, it is possible that a quantized spacetime will

lead to observable physical phenomena. A quantized spacetime

together with the prediction of a repulsive gravitational

force, predicted by the unified theory presented,

Sec. 3.2, leads to the concept of hyperspace (or parallel

space) in which the limiting speed of light is nc, with n >

1, integer and c the vacuum speed of light [9], [10].

4 A more detailed discussion will be given in our paper entitled Field

Propulsion I: Novel Concepts for Space Propulsion.

2.2 The Physics of Continuous Spacetime

Einsteinian spacetime [11], [12] is indefinitely divisible

and can be described by a differentiable manifold. In reality,

however, spacetime is a quantized field. Gra-vitation

is the dominant force in systems on astronomical scales.

GR can be summarized in the single sentence: matter

curves spacetime. For a flat geometry, the angles of a triangle

add up to 180 degrees. The spacetime metric of a

flat universe is given by

ds2=dx2dy2dz2−c2dt2 .

On the surface of a sphere spherical coordinates are used

ds2=dr2r2d 2r2sin2d 2−c2dt2 .

For a generally curved spacetime the metric is written in

the form (double indices are summed over)

ds2=gdxdx

where g is the metric, x1, x2, x3 are the spatial coordinates,

and x4 is the time coordinate 5. The cosmo-logical

principle states that the Universe does not have preferred

locations (homogeneous) or directions (isotropic). Therefore

the spatial part of the metric has constant curvature.

Extending the spherical metric, the most general metric is

given by the Robertson-Walker metric

ds2=a2 t [ dr2

1−k r2r2 d 2sin2d 2]−c2dt2 ,

where a(t) is the scale factor of the Universe. Here it is

assumed that the Universe started from a fixed size x0 and

expanded according to a(t). Two points that were at distance

x0 at time t0, now are at distance x(t) = a(t) x0.

In 1994 Alcubierre [13], [14] specified the following metric,

termed the warp-drive spacetime

ds2=[dx2−V s f  rsdt2dy2dz2]−c2dt2 ,

where Vs(t) is the velocity along a given curve xs(t) 6 and

s(t) = (x-xs(t))2 + y2 + z2. A choice for fs(t) is fs = (1-rs/R)4

and R is a distance. Without proof it is stated that, if this

warp-drive metric could be generated - the term metric

engineering was coined - around a spaceship, the vehicle

would be traveling faster than the speed of light, seen

from a spacetime diagram of flat space. Locally the ship

is moving less than the speed of light. A bubble of spacetime

curvature must surround the spaceship. Since the Alcubierre

metric requires a negative local energy density, it

cannot work in GR. Quantum mechanics allows negative

energy density, and perhaps a combination with the quintessence

particle, see Fig. 2, the sixth fundamental force

predicted by EHT. It is interesting to note that the experi-

5 Often the time coordinate is denoted as x0.

6 For simplicity y = 0 and z = 0 are assumed.

ment by Tajmar et al. [15] could be interpreted as metric

engineering since an artificial gravitational field was generated

and, as a result, the local metric has been changed.

There are also spacetime concepts of higher dimen-sionality.

Kaluza (1921) introduced an additional fourth spatial

dimension into Einstein's field equations, and in a letter

to Einstein pointed out that Maxwell's theory of electromagnetism

was comprised in the now 5-dimen-sional

Einstein equations. However, his theory produced divergencies

and could not answer the question about the visibility

of this 5th dimension. In 1926 Klein, a Swedish

physicist, introduced the concept of a curled up dimension

that exists on the Planck length scale only, and thus

cannot be observed by experiment. String theory [16], see

Sec. 3.1, has extended this concept by intro-ducing 8 additional

spatial dimensions, resulting in a total of 11 spatial

dimensions.

3 Quantized Spacetime

In the following it is shown that the combination of

quantum theory (Heisenberg's uncertainty relation) with

special relativity (constancy of the speed of light and

E = m c2) and general relativity (Schwarzschild radius)

directly leads to a quantized spacetime, resulting in the

well known Planck scales. The proof is straightforward

and is given below. The quantization of spacetime leads

to the proposition of a hyperspace (parallel space) in

which superluminal speeds should be possible, see [17].

Heisenberg´s indeterminacy (uncertainty) relation, for instance

relating time and energy indeterminacies,

tEℏ , allows for arbitrarily small Δt by making

the energy uncertainty arbitrarily large. However, this is

not the case in the real physical world. It is straight-forward

to prove the discreteness of spacetime. To this end,

the time measurement process using clocks is analyzed

[18]. Einstein's GR itself is used to disprove the existence

of continuous spacetime. According to Einstein, the energy

of any material object is E = mc2. The smallest time

interval, δt, that can be measured must of course be larger

than the time uncertainty required to satisfy Heisenberg's

uncertainty relation that is tt=ℏ/E. A clock of

mass m cannot have an energy uncertainty ΔE > mc2, because

this would lead to the creation of additional clocks,

hence tt=ℏ/mc2 . A clock of length l needs a

measuring time c δt > l in order to receive the measuring

signal. A characteristic length of a material body is its

Schwarzschild radius, namely when its gravitational energy

equals its total energy mc2, i.e., rS = Gm/c2. This

means for the mass of the clock m < rS c2/G, because the

body must not be a black hole from which signals cannot

escape. Inserting the value l for rS , m < δt c3/G. Inserting

the value of m in the above relation for δt, one obtains the

final relation t2ℏG/c5. Thus the quantization aspect

of the GODQ principle, which comprises the four basic

physical principles of Nature, see Sec. 3.2.1, directly

delivers a fundamental lowest limit for a time interval,

termed the Planck time. In a similar way the smallest

units for length and mass can be found. As shown above,

Planck units are constructed from the three fundamental

constants in Nature, namely ℏ, c, and G. The values for

the Planck units are:

• Planck mass mp = (c/G)1/2 = 2.176 ´ 10-8 kg,

• Planck length lp = (Gℏc-3)1/2 = 1.615 ´ 10-35 m,

• Planck time tp = (Gℏ/c5)1/2 = 5.389 ´ 10-44 s.

This means that the classical picture of points in a continuous

spacetime does not make physical sense. Physics below

the Planck units is not possible, since one cannot distinguish

between vacuum and matter. No measurements

are possible. The nature of spacetime is discrete in the

same way as energy is discrete, expressed by E = h.

Since spacetime therefore is a quantum field, it should

have corresponding quantum states, described by a quantum

field theory. Since spacetime is equivalent to gravity,

gravity itself needs to be described by a quantum field

theory. In both classical physics and quantum mechanics

point particles are used, and the inverse force law leads to

infinities of type 1/0 at the location of the particle. As was

shown above, any particle must have a discrete geometric

structure, since it is finite in size. The minimal surface

must be proportional to the Planck length squared. From

scattering experiments, however, it is known that many

particles have a much larger radius, for instance, the proton

radius is some 10-15 m, and thus its surface would be

covered by about 1040 elemental Planck surfaces. Hence,

an elementary particle must be a highly organized and

also complex geometrical structure. It is therefore mandatory

that point particles are banished. In addition, the organizational

state of an entity or structure needs to be

measured and therefore, among other reasons, the concept

of an organization coordinate in an internal space (de-

Figure 1: This picture, taken from Wikipedia, shows

three types of possible geometries for the Universe,

namely closed, open, or flat. At present, a flat Universe

is assumed.

scribing the additional degrees of freedom) is introduced,

see Sec. 3.2.1.

3.1 Spacetime of Higher Spatial Dimensions:

String Theory

The theory by Kaluza and Klein (1921, 1926) already introduced

a fourth spatial dimension to account for electromagnetism.

According to string theory, electrons are not

point particles, but are vibrations of a string, whose length

is at the Planck scale, some 10-35 m. Strings are one-dimensional

entities. Modifying the vibrations frequency of

these strings they can turn into other particles, for instance,

the electron can turn into a neutrino, or into any of

the known subatomic particles. String theory leads to a

unification of the four fundamental interactions, but requires

11 real spatial dimensions, [16]. However, because

of the discrete nature of spacetime there seems to be no

need for string theory, which replaces point particles by

strings, but requires hitherto unobserved additional spatial

dimensions.

However, there is a fundamental difference compared to

the concept of spacetime with internal dimensions, in that

strings are objects in spacetime, while in the next section

a geometrization concept is employed that explains all

particles as geometric objects constructed from spacetime

itself.

3.2 Spacetime with Internal Dimensions

However, there exists another concept, coming from the

idea that elementary particles have additional degrees of

freedom in some kind of internal space. Therefore, the

concept of physical space as the combination of spacetime

and internal space is introduced. This marriage of 4-

dimensional spacetime with internal space is called fiber

bundle space mathematically. In the following the term

physical space will be used for this combination, since

all the fundamental forces of physics will be described in

this space. These internal degrees of freedom can then be

connected with the dynamical motion in spacetime. This

is the geometrical structure utilized in gauge theory. The

dimension of the internal space and its symmetries determine

the physics that is possible. In order to have a unified

field theory the proper internal space has to be constructed

that encompasses all interactions of physics. In

the next section, GR is equipped with an 8-dimensional

internal space (all internal coordinates have negative signature),

termed Heim space. Once this internal space is

included, all physical interactions are fixed. There is only

one single selection rule used to selecting internal subspaces.

It turns out that six fundamental physical interactions

should exist.

3.2.1 Extended Heim Theory

In EHT a set of 8 additional coordinates is introduced, but

contrary to String theory, the theory postulates an internal

space with 8 dimensions that governs physical events in

our spacetime (actually a manifold M4 ).The crucial point

lies in the construction of the internal space that should

come from basic physical assumptions, which must be

generally acceptable. In EHT, an 8-dimensional space is

constructed, termed Heim space, H8 that is missing in GR.

In other words, GR does not possess any internal space,

and thus has a very limited geometrical structure, namely

that of pure spacetime. Because of this limitation, GR

cannot describe the fundamental forces in physics and

consequently has to be extended. The extension as done

in EHT, lies in the introduction of the internal space H8.

EHT reduces to GR when this internal space is omitted.

The metric tensor, as used in GR, has purely geometrical

means that 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. Stated

in simple terms: matter curves spacetime. 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.

Figure 2: EHT has, as one of its most important consequences,

the prediction of two additional, gravitational like interactions

and the existence of two messenger particles, termed

gravitophoton and quintessence.

According to the quantization principle, the minimal

length in the space part of H8 is the Planck length. Applying

the geometrization rule of the GODQ principle, see

below, Planck mass and Planck time are converted into

length units leading to two additional lengths constants

lpm = ħ/mpc and lpt = ctp that have the same numerical value

as lp but define two additional different length scales,

relating lengths with time units as well as length with

mass units. The introduction of basic physical units is in

contradiction to classical physics that allows infinite divisibility.

As a consequence, measurements in classical

physics are impossible, since units cannot be defined.

Consequently, Nature could not provide any elemental

building blocks to construct higher organized structures,

which is inconsistent with observation. Thus the quantiza-

tion principle is fundamental for the existence of physical

objects. Therefore the three Planck length units as defined

above must occur in the structure of both spacetime and

internal space H8. In spacetime length unit lp is the basic

unit for the spatial coordinates and lpt measures the time

coordinate. In order to connect geometry with physical

entities, in the internal symmetry space coordinates i

are measured in units of lpm. Hence all lengths in H8 are

represented by multiples of 1/mp, and therefore internal

coordinates i are denoted as energy coordinates. In

other words, the concept of energy coordinate ensures

that an inverse length is representing a physical mass.

Since length values are quantized, the same holds for

physical mass. In this regard the connection of geometry

with physical objects has been established, but, in order to

achieve this goal, the quantization principle had to be introduced

ab initio.

In contrast to Einstein, EHT is based on the following

four simple and general principles, termed the GODQ

principle of Nature7.

i. Geometrization principle for all physical interactions,

ii. Optimization (Nature employs an extremum

principle),

iii. Dualization (duality, symmetry) principle (Nature

dualizes or is asymmetric, bits),

iv. Quantization principle (Nature uses integers

only, discrete quantities).

From the duality principle, the existence of additional internal

symmetries in Nature is deduced, and thus a higher

dimensional internal symmetry space should exist, which

will now be determined.

In GR there exists a four dimensional spacetime, comprising

three spatial coordinates, x1, x2, x3 with positive signature

(+) and the time coordinate x4 with negative signature

(-). It should be remembered that the Lorentzian metric of

ℝ4 (actually spacetime is a manifold M4) has three spatial

(+ signature) and one time-like coordinate (- signature)

[19]. The plus and minus signs refer to the metric that is,

the spatial components are taken to be positive and the

time coordinate is negative. 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 c.

Hence a general coordinate system in ℝ4 (M4) comprises

the curvilinear coordinates8 xm with m=1,..,4. Next, the coordinate

structure of H8 is determined. Coordinates in H8

are denoted as i , and are termed internal coordinates

with =1,, 8. This set of 8 coordinates will now be

7 This will be discussed in detail in our forthcoming paper: Field propulsion

I: Novel Physical Concepts for Space Propulsion.

8 coordinates xμ can also be Cartesian. Meaning of coordinates will be

clear from the context.

determined by utilizing the GODQ principle introduced

above. To this end, the second law of thermodynamics is

considered, which predicts the increase of entropy. Everywhere

in Nature, however, highly organized structures

can be found like galaxies, solar systems, planets, plants

etc., which, according to the duality principle, have to be

introduced into a unified theory. A description of Nature

that only provides a route to decay or to lower organizational

structures is in contradiction to observation. Therefore,

an additional, internal (negative signature-) coordinate,

termed entelechial coordinate, 5 , is introduced.

The entelechial dimension can be interpreted as a measure

of the quality of time varying organizational

structure (inverse or dual to entropy). It should be mentioned

that all other additional internal coordinates have

negative signature, too. Second, when the universe was

set into motion, it followed a path marked by a state of

great order. Therefore, to reflect this generic behavior in

Nature, the aeonic dimension, 6 , is introduced that is

interpreted as a steering coordinate toward a dynamically

stable state. On the other hand, the entropy principle

is firmly established in physics, for instance in

- decay. Entropy is directly connected to probability,

which in turn is related to information. Therefore, two additional

coordinates 7 ,8 are needed, which are complementary

to the organizational coordinates, to reflect

this behavior of Nature, termed information coordinates

that are describing information waves. Finally, since both

space and time are essential in the evolution and decay of

structures, the internal symmetry space possesses a total

of 8 coordinates. In summary, coordinates  with

=1,, 4 denote spatial and temporal coordinates,

 with =5, 6 denote entelechial and aeonic coordinates,

and  with =7,8 denote information coordinates

in H8. The name gravitophoton has been chosen

because of the type of interaction, namely a transformation

of the electromagnetic field (photon) into the gravitational

field (gravitophoton). The arrow between the

gravtitophoton and electromagnetic boxes indicates the

interaction between the messenger particles that is, photons

can be transformed into gravitophotons. In the same

way the quintessence interaction can be generated from

gravitons and positive gravitophotons (repulsive force).

Heim space, H8 comprises four subspaces, namely ℝ3, T1,

S2, and I2. In the set of metric-subspaces that can be constructed,

where each element is denoted as a hermetry

form. Each hermetry form has a direct physical meaning,

for details see refs. [9], [20]. In order to construct a hermetry

form, either internal space S2 or I2 must be present.

In addition, there are three degenerated hermetry forms

that describe partial forms of the photon and the quintessence

potential. They allow the conversion of photons

into gravitophotons as well as of gravitophotons and

gravitons into quintessence particles. There exist 15 hermetry

forms, six of them describe the messenger particles

of the fundamental interactions. Hermetry forms H5,

H11, and H12 are used to describe the gravitational messenger

particles. In a very recent announcement by the

European Space Agency, 23 March 2006, the measurement

of an artificial gravitational field was reported, generated

by a rotating superconducting ring.

4 Propulsion Concepts from Spacetime

Physics

4.1 Metric Transformation (Transmutation)

In a recent experiment, funded by the European Space

Agency and the Air Force Office of Scientific Research,

Tajmar et al. ref. [15] report on the generation of a toroidal

(tangential, azimuthal) gravitational field in a rotating

accelerated (time dependent angular velocity) superconducting

ring. This would be the first time that an artificial

gravitational field is generated and, if correct, would have

great impact on future technology. Furthermore, the experiment

would demonstrate the conversion of electromagnetic

interaction into a gravitational field. This is exactly

the effect that is predicted by EHT, and both a qualitative

and quantitative explanation of this effect will be

given below. Since the experiment generates a tangential

gravitational field, it cannot be used directly as a propulsion

system. It is, however, of great importance, since it

shows for the first time that a gravitational filed can be

generated other than by the accumulation of mass. In this

section we will also discuss the validity of the physical

explanation, namely the Higgs mechanism to be responsible

for the graviton to gain mass, given by Tajmar and de

Matos [15], which they termed the gyromagnetic London

effect. According to these authors, this effect is the physical

cause for the existence of the measured gravitational

field.

The arguments of these authors are ingenious, but there is

some doubt whether the linearized Einstein equations, see

Eqs. (1, 2), can be used in the explanation of this effect.

Although these equations are predicting such a phenomenon,

the effect is 20 orders of magnitude smaller than the

observed one, and thus would be completely unobservable.

In the derivation, a magnetic field is set equivalent

to a gravitational field. This assumption of transforming a

magnetic field into a gravitational field is not compatible

with current physics.

Instead, the Heim-Lorentz force, as predicted by EHT but

now using a coupling to bosons (Cooper pairs), is used to

explain this effect. Deriving this effect from gravitophoton

interaction, a physical interpretation can be given that

explains both qualitatively and quantitatively the experimental

results. Moreover, theoretical considerations obtained

from EHT lead to the conclusion that a modified

experiment will generate a gravitational field acting

parallel to the axis of rotation of the ring (torus), see

Fig. 3, and thus can serve as a field propulsion principle9.

In this experimental configuration the superconducting

rotating ring is replaced by an insulating disc and a set

of superconducting coils as depicted, in principle, in Fig.

3. EHT allows to calculate the acceleration force and also

provides the guidelines for the construction of a propulsion

device. The actual experimental setup differs from

the simple configuration of the cover picture, but the principle

remains unchanged. According to the predictions of

EHT experimental requirements, i.e., magnetic field

strength, current densities and number of turns of the solenoid,

are substantially lower than for fermion coupling

that was assumed in all our papers so far, see refs. [9],

[10], [20].

Figure 3: The picture shows the physical principle of the experimental

setup to generate a gravitational field in the z-direction

(upward, above rotating disk) by the Heim-Lorentz

force using a superconducting coil (boson coupling) and a

rotating disk or ring. The actual experiment would be somewhat

different.

The superconducting current loop (blue), see Fig. 3, provides

an inhomogeneous magnetic field at the location of

the rotating disk (red). The z-component of the gravitophoton

field, bz is responsible for the gravitational field

above the disk. This experimental setup also serves as the

field propulsion device, if appropriately dimensioned.

4.1.1 Description of the Gravitomagnetic Field

Experiment

The materials for which a strong gravitational acceleration

was measured were niobium (Nb, TC=9.4 K) and lead

(Pb, TC = 7.2 K). No gravitational field was measured in

YBCO (Yttrium barium copper oxide, YBa2Cu3O7-x, TC =

94 K) and BSCCO (Bismuth strontium calcium copper

oxide, Bi2Sr2CanCun+1O2n+6, TC=107 K) which are so

called high-temperature superconductors whose critical

9 A detailed discussion will be given in our forthcoming paper entitled

Artificial Gravitational Fields.

 

ez

er

e

current density is substantially lower than that for Nb or

Pb.

Considering the Einstein-Maxwell formulation of linearized

gravity, a remarkable similarity to the mathematical

form of the electromagnetic Maxwell equations can be

found. In analogy to electromagnetism there exist a gravitational

scalar and vector potential, denoted by g and Ag,

respectively, see [21]. Introducing the gravitoelectric and

gravitomagnetic fields

e=−∇g and b=∇×Ag (1)

the gravitational Maxwell equations can be written in the

form

∇⋅e=−4G ,∇⋅b=0

∇×e=0 ,∇×b=−16G

c2 j

(2)

where j= v is the mass flux and G is the gravitational

constant10. The field e describes the gravitational field

form a stationary mass distribution, whereas b describes

an extra gravitational field produced by moving masses.

At critical temperature Tc some materials become superconductors

that is, their resistance goes to 0. Superconductors

have an energy gap of some Eg  3.5 kTc . This

energy gap separates superconducting electrons below

from normal electrons above the gap. At temperatures be-

10 Here no consideration is given to the fact that G comprises three

parts according to EHT.

low Tc , electrons are coupled in pairs, called Cooper

pairs, which are bosons. The exact formation of Cooper

pairs is not known. The coupling of the electron pairs

seems to be via phonons, generated by electron movement

through the lattice of the superconductor. The size

of a Cooper pair is some 103 nm. The crystal lattice contains

defects that lead to an energy transfer E from the

electron gas to the lattice. E must be smaller than Eg

otherwise the Cooper pairs are destroyed.

The speed of the Cooper pairs can be calculated in a coordinate

system where the electron gas is at rest and the lattice

is moving, applying classical energy and momentum

conservation. Decelerating the grid means that Cooper

pairs gain energy. The maximum amount of energy that a

Cooper pair can absorb is Egap , otherwise it is lifted in the

band above, and superconductivity is lost. Therefore the

simple ansatz for the maximum energy gap

1/2mvc

2=Egap=3.5 k T c can be used, vc denoting the

velocity of a Cooper pair. At temperature Tc = 10 K a

speed of vc = 104 m/s is obtained. A smaller band gap

therefore cause a decrease in the speed of the Cooper

pairs. Quantum mechanics calculations yield a more correct

value of some vc = 105 m/s.

4.1.2 Field Propulsion

Fig. 3 describes the experimental setup for which an insulating

disk rotates above a superconducting solenoid. Fig.

4 depicts the experiment of Tajmar et al., where a superconducting

ring is subject to angular acceleration. In both

cases a gravitophoton force arises. EHT makes the following

predictions for the gravitational fields generated

by the gravitophoton force.

• In the first case, the gravitophoton force produces

a gravitational force above the disk in the zdirection

upward and also in the radial direction.

• In the second case, the gravitophoton force is in

the azimuthal direction only (experiment by Tajmar

et al.).

It is well known that a rotating superconductor generates

a magnetic induction field, the so called London moment

B=−

2me

 (3)

where ω is the angular velocity of the rotating ring and e

denotes elementary charge. It should be noted that the

magnetic field in Tajmar's experiment is produced by the

rotation of the ring, and not by a current of Cooper pairs

that are moving within the ring. This is a major difference

between the experiment of Fig. 3 and the proposed experiment

depicted in Fig. 4. Therefore the velocity of the

Cooper pairs with regard to the lab system is given by rω

in the experiment of Fig. 3 while the maximal velocity of

Cooper pairs in Fig. 4 is given by the maximum energy

ez

er

e

Figure 4: Rotating superconducting torus (Niobium) modified

from Tajmar et al. All dimensions are in mm. A cylindrical CS

(r, θ, z) with origin at the center of the ring is used. In Ring

accelerometers measured a gravitational acceleration of some

100 μg in the azimuthal (tangential, θ) direction when the ring

was subject to angular acceleration, ˙ . No acceleration

was measured in the z-direction (upward). If the direction of

rotation is reversed, the acceleration field changes sign, too.

gap, respectively its quantum mechanical counterpart.

The major difference between the two experiments lies in

the generation of the magnetic induction field B. Tajmar

and his colleagues simply postulate an equivalence between

the generated B field, Eq. (3) with a gravitational

field by proposing a so called gravitomagnetic London effect.

However, this transformation between electromagnetics

and gravitation is introduced ad hoc and contradicts

current physics, since the four known physical forces

do not allow such a direct coupling.

On the other hand, this kind of coupling is a basic fact of

EHT, because of its six fundamental interactions, which

foresee such a conversion of hermetry form H7, describing

photons, into the hermetry form H5, describing the

gravitophoton interaction.

Let R denote the radius of the rotating ring, then Eq. 3

puts a limit on the maximal allowable magnetic induction,

Bmax, which is given by

Bmax

2 =14

k BT C

R2 . (4)

If the magnetic induction exceeds this value, the kinetic

energy of the Cooper pairs exceeds the maximum energy

gap, and the Cooper pairs are destroyed. The rotating ring

is no longer a superconductor. Moreover, the magnetic induction

must not exceed the critical value BC(T), which is

the maximal magnetic induction that can be sustained at

temperature T, and is dependent on the material. EHT predicts

that the magnetic induction field B is equivalent to a

gravitophoton (gravitational) field bgp . Therefore, the following

relation holds, provided that B is smaller than Bmax

bgp∝ B

Bmax

B (5)

As soon as B exceeds Bmax the gravitophoton field vanishes.

From EHT the following general relationship between

a magnetic and the neutral gravitophoton field, bgp, can be

derived

bgp= 1

1−k 1−ka

−1 em

Bmax

B (6)

where k = 1/24 and a = 1/8. The dimension of bgp of is s-1.

Inserting Eq. 3 into Eq. 6, using Eq. 5, and differentiating

with respect to time, results in

∂bgp

∂ t

= 1

1−k 1−ka

−1 2e

Bmax

∂ B

∂t

. (7)

Integrating over an arbitrary area A yields

∫∂ bgp

∂t

⋅d A=∮g gp⋅d s (8)

where it was assumed that the gravitophoton field, since it

is a gravitational field, can be separated according to Eqs.

(1, 2). Since the above formulas will be applied to the experimental

configurations depicted in Figs. 3 and 4, cylindrical

coordinates r, θ, z are employed. ggp is the acceleration

field generated by the gravitophoton field. Combining

Eqs. 7 and 8 gives the following relationship

∮ ggp⋅d s= 1

1−k 1−ka

−1 2e

∫ B

Bmax

∂ B

∂t

⋅d A (9)

From Eq. 3 one obtains

∂ B

∂t

=−

2me

e ˙ (10)

Next, we apply Eqs. 9 and 10 to the experimental configuration

of Fig. 3, calculating the gravitophoton acceleration

for the in-ring accelerometer. It is assumed that the

accelerometer is located at distance r from the origin of

the coordinate system. From Eq. 3 it can be directly seen

that the magnetic induction has a z-component only. From

Eq. 9 it is obvious that the gravitophoton acceleration is

in the r-θ plane. Because of symmetry reasons the gravitophoton

acceleration is independent on the azimuthal angle

θ, and thus only has a component in the circumferential

(tangential) direction, denoted by e . Since the gravitophoton

acceleration is constant along a circle with radius

r, integration is over the area A=r2 ez . Inserting

Eq. 10 into Eq. 9, and carrying out the integration the following

expression for the gravitophoton acceleration is

obtained

ggp=− 1

Bmax

˙ r (11)

where the minus sign indicates an acceleration opposite to

the original one and it was assumed that the B field is homogeneous

over the integration area. Now the experimental

values taken from the paper by Tajmar et al. will be inserted.

The following values are used:

˙ =103rad /s2 ,r=3.6×10−2m ,B/ Bmax=3.97×10−4

where the angular acceleration was determined from the

slope fit of Fig. 6 in ref. [15] and the r value was determined

from Fig. 4 (R = 36 mm). The ratio of the magnetic

fields was calculated from the following formula, obtained

by dividing Eq. 3 by the square root of Eq. 4

Bmax

= 1

7  me

k BT C 1/ 2

R. (12)

Inserting an estimated average value of ω = 175 rad/s,

me = 9×10-31 kg, kB=1.38×10-23 J/K, TC = 9.4 K, and

R = 7.2×10-2 m, this ratio is calculated as 3.97×10-4. From

Fig. 6 in ref. [15] an experimental value of about 1.0×10-4

g was determined. Inserting the proper values into Eq. 11

finally delivers the theoretical value of the gravitophoton

acceleration for the experiment by Tajmar et al.

ggp=1.3×10−4 g . (13)

Compared to the theoretical value of Eq. 13 there is a

close agreement between the predicted gravitophoton

force and the measured acceleration. It should be kept in

mind that the exact angular velocity was not known and

an average value of 175 rad/s was used. Considering both

the mathematical and physical complexity of the derivation

the closeness of theory and experiment is remarkable.

The results might need to be adjusted for the exact experimental

values. It should be noted that values of k and a

have been derived some ten years ago and are published

in [22]. No parameter was adjusted in the derivation of

Eq. 11. Moreover, the theory also correctly predicts direction

and sign of the acceleration field. This is seen as a

sign that the predicted six fundamental interactions may

exist in Nature.

4.1.3 Space Device Based on Field Propulsion

The experiment by Tajmar et al. generates an azimuthal

gravitational field, and thus is not suitable for propulsion.

The lesson learned from the experiment by Tajmar et al.

is the fact that the coupling to bosons (Cooper pairs) is of

prime importance. However, employing the general

Heim-Lorentz force equations to the experimental setup

of Fig. 3, Heim-Lorentz force now produces force components

in the radial r and z- directions. These components

are given by

Fr er=

me v

T bz e×ez  (14)

F z ez=

v

mn v

T bz e×ez ×e

(15)

where vC is the velocity of the Cooper pairs in the superconducting

solenoid (Fig. 3), v

T=10m/ s 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. In contrast to the fermion coupling,

experimental requirements are modest. The following

assumptions were made: N=100 number of turns of

the solenoid, current of some 1-2 A (needed to calculate

bz), diameter of solenoid 0.1 m. A detailed analysis predicts

an acceleration in z-direction of some 6.0×10-5 g.

From these numbers it is clear that, if theoretical predictions

are correct, the realization of a workable space propulsion

device that can lift itself from the surface of the

Earth seems to be feasible.

Conclusions and Future Work

In this paper an overview of the current status of space

propulsion was given. It has been shown that even with

an advanced fission propulsion system, space travel will

be both very limited and very costly. Travel time to other

planets will remain high. Metric engineering of spacetime

or using wormholes does not seem to be technically feasible.

On the other hand, the recent experiment by Tajmar,

if confirmed, has shown that a coupling between electromagnetism

and gravitation exists, which allows the generation

of artificial gravitational fields. EHT, which uses an

internal 8-dimensional space, has predicted this kind of

coupling and foresees six fundamental physical interactions.

The theory was successfully applied to predict the

outcome of Tajmar's experiment and also provides guidelines

for an experimental setup that can be used as field

propulsion device. Research therefore should focus on the

refinement of the experiment as well as on the theoretical

foundation of EHT.

References

1. Villard, R., L.R. Cook: Infinite Worlds, Univ. California

Press, , 2005.

2. Zaehringer, A.: Rocket Science, Apogee Books, Chap 7.,

2004.

3. Mallove, E. and G. Matloff: The Starflight Handbook, Wiley,

Chap. 3, 1989.

4. Jahnshan, S.N. and T. Kammash: Multimegawatt Nuclear

Reactor Design for Plasma Propulsion Systems, Vol 21,

Number 3, May-June 2005, pp.385-391.

5. Emrich, W.J. and C. W. Hawk: Magnetohydrodynamic Instabilities

in a Simple Gasdynamic Mirror Propulsion System,

Vol 21, Number 3, May-June 2005, pp.401-407.

6. Czysz, P.A., C. Bruno: Future Spacecraft Propulsion Systems,

Springer, 2006.

7. Krauss, L.M.: Propellantless Propulsion: The Most Inefficient

Way to Fly?, NASA TM/CP 208694, January 1999.

8. Rovelli, C.: Loop Quantum Gravity, IoPNovember 2003 .

9. Dröscher, W., J. Hauser: Heim Quantum Theory for Space

Propulsion Physics, pp. 1430-1441, AIP, 2005.

10. Liddle, A.: An Introduction to Modern Cosmology, Wiley,

2003.

11. Witten, E.: Reflection on the Fate of Spacetime, Physics Today,

1996.

12. Hartle, J.B.: Gravity, Addison Wesley, 2003.

13. Vass, R.: Tunnel durch Raum und Zeit, Kosmos, Stuttgart,

2005.

14. Heim, B.: Vorschlag eines Weges einer einheitlichen Beschreibung

der Elementarteilchen, Z. für Naturforschung,

32a, pp. 233-243, 1977.

15. Tajmar, M. et al.: Experimental Detection of the Gravitomagnetic

London Moment, arXiv, gr-qc/06030332006.

16. Zwiebach, R.: Introduction to String Theory, Cambridge

Univ. Press, 2004.

17. Dröscher, W., J. Hauser: Magnet Experiment to Measuring

Space Propulsion Heim-Lorentz Force, 41st JCP, AIAA

2005- 4321, 10 pp., Tucson, AZ, 10-13 July, 2005.

18. Schiller, C.: Motion Mountain, The Adventure of Physics

(Chap. XI), September 2005, www.motionmountain.net.

19. Carrol, S. M.: Spacetime and Geometry, Addison-Wesley,

San Francisco, 2004.

20. Dröscher,W., J. Hauser: Guidelines for a Space Propulsion

Device Based on Heim's Quantum Theory, 40 th JCP, AIAA

2004-3700, 21 pp., Ft. Lauderdale, FL, 7-10 July, 2004.

21. Hobson,M.P., Efstathiou, G., and A.N. Lasenby: General

Relativity, Cambridge University Press, 2006.

22. Heim, B., Dröscher, W: Strukturen der Physikalischen Welt

und ihrer nichtmateriellen Seite, Resch Verlag1996.

AIAA2006-4608LetterShortVersion.pdf (5 MB)

Gravitational Field Propulsion

02.05.2014 14:27

AIAA-2009-5069-885Gravitational_Field_Propulsion.pdf (5,1 MB)

Gravitational Field Propulsion

Walter Dröscher1, Jochem Hauser 2

1Institut für Grenzgebiete der Wissenschaft, 6010 Innsbruck, Austria

2Faculty Karl-Scharfenberg, Univ. of Applied Sciences, Salzgitter Campus, 38229 Salzgitter, 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 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 fields by man made

devices. In other words, gravity fields should be experimentally controllable. At present, it is believed that there

are four fundamental interactions in physics: strong (nuclei), weak (radioactive decay), electromagnetic and

gravitational. 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 the 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. However, recently, novel physical concepts were presented that might lead to

advanced space propulsion technology, based on two novel fundamental force fields. These forces are 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. The current theoretical and experimental concepts pertaining to

the novel physics of these gravity-like fields are discussed together with recent gravitomagnetic experiments

performed at ARC Seibersdorf (2008). The theoretical concepts of Extended Heim Theory, EHT, are employed

for the explanation of these experiments.

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

2 Prof., Faculty Karl-Scharfenberg, Univ. of Applied Sciences, 38229 Salzgitter, Senior member AIAA.

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American Institute of Aeronautics and Astronautics

45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit

2 - 5 August 2009, Denver, Colorado

AIAA 2009-5069

I. Experimental and Theoretical Concepts of Novel Field 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.,17 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 achieved. 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 kind of interstellar travel might be unfeasible.

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

is, there is a belief only on 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 that is, there might exist additional long range interactions. This question was already discussed

in detail in several recent papers, for instance9, 12–14 . Since 2002, novel physical ideas have been presented under

the name Extended Heim Theory, (EHT), a, 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 forces.

Beside Newtonian gravitation (graviton, ng, attractive), EHT requires the existence of two additional gravitational

fields, termed gravitophoton interaction, n0

gp (both attractive and repulsive), which results from the conversion of

electromagnetic energy into gravitational energy, and quintessence, nq, (repulsive)9, 12 . The geometric approach,

namely describing physical interactions by metric tensors and the underlying physical concepts of EHT are briefly

presented in Sec. II.

The question naturally arises about the physical relevance of theses ideas. 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

b, performed at ARC Seibersdorf, Austria. Since then further experimental results have been published by Tajmar et

al. from ARC29–31 and, in July 2007, Graham et al. published a paper on the generation of a gravitomagnetic field

aIt should be noted thatEHT does not have reached the status of physical theory. At present, it is a classification scheme to construct a polymetric

tensor that possibly encompasses all physical interactions9, 12, 13 and is an approach to geometrize physics as envisaged by Einstein16 as well

as Heim18 in 1952 and Finzi27 in 1955.

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 a stationary mass. The term gravitomagnetic force is used if EG = vBG , i.e.

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

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Figure 1. The picture shows the rapidly increasing mission difficulty and hazard with 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 posed by the currently four known fundamental physical interactions.

produced by a cryogenic lead disk, but using a completely different measurement technique32 , see Table 4 . 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 ARC. In addition, in 2008 Tajmar et al.33 published a more comprehensive set of gravitomagnetic

experiments. In Sec. III, EHT will be used to present a qualitative explanation for these results. Furthermore, in 2007

results of the NASA Stanford Gravity-Probe B (GP-B) experiment15 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 pairs9 .

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.

II. Physical Concepts of EHT for Gravitational Field Propulsion

The physical concepts of EHT were laid out in previous publications, see for instance9, 12–14 . The interpretation

of the physical equations for the postulated gravitophoton field leads to the conclusion that this field could be used

to accelerate a material body without the use of propellant by generating a vertical gravitational field. Therefore,

gravitation, as we know it seems to be composite, and according to EHT comprises three interactions, mediated by

the graviton (ng; attractive), gravitophoton (n0

gp; attractive and repulsive), and the quintessence or vacuum (nq;

repulsive) particle that is, there there should be three field quanta of gravitation. This means that the gravitational

constant G contains contributions of all three gravitational constants, termed Gg;Ggp and Gq, respectively.

A. The Nature of Gravity

In EHT two additional gravity-like fields occur, and therefore the set of three coupled fields needs to be considered.

Moreover, a conversion of photons, g into gravitophotons, n0

gp, can take place, coupling electromagnetism with gravitation,

which leads to the generation of strong gravitomagnetic fields in comparison with GR. Hence, classical physics

as conceived by EHT may, under special experimental conditions, lead to hitherto unknown phase transitions, and

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thus exhibit completely novel physical phenomena.

Because of the coupling of electromagnetism with gravitation, the complete set of of equations should be considered,

described of course by the Einstein field equations, which are the structural equations for all interactions.

However, for the time the set of gravitational equations is considered only.

• In classical GR, the Lense-Thirring frame dragging effect exists, as was confirmed by GP-B, and thus the graviton,

ng, is capable of generating both the gravitoelectric, Eg, as well as the gravitomagnetic, Bg field. In GR it is

these fields only that appear in the Einstein field equations.

• The quintessence quantum nq, as the dual exchange particle to the graviton, also should have the capability of

producing a gravitomagnetic field, termed Bq, although the interaction strength is assumed to be much smaller.

• In the gravitomagnetic experiments by Tajmar et al. (no acceleration field) a much larger gravitomagnetic field

than predicted by GR was measured, which is denoted as Bgp. Obviously, because of its magnitude, this field

is not generated by gravitons, and thus is not described by the field Bg. Consequently, the quanta of this field

are not gravitons, ng, but the above mentioned gravitophotons, n0

gp. Instead, the gravitophoton, n0

gp, is deemed

to be responsible for its existence. The gravitophoton is believed to emerge from photon conversion, i.e., from

the mechanism of converting photons into gravitophotons, which eventually leads to the strong gravitomagnetic

field observed.

Therefore the total gravitomagnetic field actually measured is

BG := Bg+Bgp+Bq; (1)

and thus should be a composite field. Clearly, it is depending on the experimental situation which of the fields is

the dominating one. In the well known situation of rotating celestial bodies, only the Bg seems to occur. In case a

phase transition occurs, in the experiments by Tajmar et al., Graham et al. and possible in the GP-B experiment,9

triggered by cryogenic temperature, the much larger Bgp seems to appear. In case quintessence quanta are generated,

the gravitomagnetic quintessence field Bq should be observed. It is assumed that the Bq field is much weaker, because

of the smaller coupling constant Gq of the repulsive quintessence force. It should be noted that only the sum of the

divergence of the three fields needs to be zero, but not for the individual fields.

It is well known that the linearized Einstein equations have a structure similar to the Maxwell equations of electrodynamics.

In EHT, these linearized equations are to be satisfied by the total gravitoelectric EG and gravitomagnetic

BG fields.

ÑBG = ÑBg+ÑBgp+ÑBq = 0 (2)

This means that a coupling between the three fields can exist. The source of one field might become the sink of another

field and mixing among the fields might occur. The mathematical implications have not yet been fully investigated.

With regard to gravitoelectric fields the situation seems to be somewhat different in that the total gravitoelectric

field EG = Eg +Eq or EG = E+

gp +E¤gp are depending on the two decay channels of the neutral gravitophoton n0

gp as

depicted in Fig.3 .

For a qualitative explanation of Tajmar’s observations, the following, somewhat hand-waving, arguments might be

considered. Could it be that in the experiments by Tajmar et al. factors c and/or G undergo drastic change, caused

by the proposed interaction between electromagnetism and gravitation, manifesting itself as phase transition ? This

process would be similar to electrodynamic phenomena in matter. If and how Maxwell’s equations are coupled to the

linearized Einstein equations, as they might, if there is an interaction between the two forces, has not been established

so far.

If spacetime is made of discrete pieces that is, atoms of spacetime exist, e.g.11 , 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.

Fig. 5 depicts the experiments of Tajmar et al., where a cryogenic Nb ring is subjected to angular acceleration,

which should lead to a gravitophoton force. EHT makes the following predictions for the measured gravitational fields

that are attributed to photon-gravitophoton interaction.

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• For the actual experiment, shown in Fig. 5 (Tajmar et al.), the gravitophoton force is in the azimuthal direction,

caused by the angular acceleration of the superconducting niobium disk. The acceleration field is opposite to

the angular acceleration, obeying some kind of Lenz rule.

• For the novel experiment of Fig. 6 (field propulsion experiment), a force component in the axial direction should

be generated.

B. 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 th interactions or material particles is described by its so called Hermetry form (hermeneutics of geometry,

i.e., in the present case 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 space12, 14), see Sec. D. 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.

C. Six Fundamental Physical Forces

The poly-metric tensor constructed in EHT gives rise to six fundamental forces (interactions) that are depicted in Fig.

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 poly-metric

tensor resulting from Heim space needs to be employed, see for instance14 .

Figure 2. Six fundamental forces are predicted by EHT. Three of them are gravity-like 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 the German physicist B. Heim. A similar principle was mentioned by the Italian

mathematician B. Finzi. The poly-metric 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,

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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. An open question still is the

mass spectrum of elementary particles, which should be obtained from an eigenvalue equation and also the lifetimes

of particles. This is, in a nutshell, the strategy chosen, based on the ideas of Heim and Finzi, to accomplish Einstein’s

goal of the geometrization of physics c.

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 staffage36 . 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 pointlike elementary particle is highly useful as a working hypothesis in particle physics.

D. 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 in9, 12–14 . Contrary to the ideas

employed in String theory, see for example37 , H8 is an internal space of 8 dimensions comprising four subspaces

denoted R3 , T1 , S2 , I2 .

In mathematical terms, H8 is the direct sum of 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 jai 2 H8 is unique. With the introduction of the four subspaces of

H8 a symmetry breaking has been introduced, which is causing the formation of physical entities as well as physical

structures via Hermetry forms, see below.

In physical terms, the R3 coordinates are responsible for the existence of mass, T1 coordinate for the existence

of charges, S2 for the formation of organizational structures, and I2 for information structures.

This symmetry breaking has been introduced ad hoc, to account for the fact that the Universe in its evolution has

the possibility to develop massive particles as well as charges. This is, however, entirely justified by observations.

H8 is supposed to be a vector space over the field of quaternions H. The elements of H8 are vectors of quaternions,

their dimension being equal to one of the four subspaces. The internal coordinates x a with a = 1; :::;8 are the real part

of the quaternions. Quaternions q = a+ib+c j+dk (qq 2 R) are an extension of the complex numbers c = a+ib by

defining two additional imaginary units j and k, where, however, k := i j; i2 = ¤1; j2 = ¤1; i j+ ji = 0. The algebra H

is the simplest non-commutative algebra possible.

To each Hermetry form, 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, ng, Hermetry form H1, is described by the group of spacetime symmetries (Lorentz and

Poincaré) SO(3;1) and P(3;1). The photon, g, denoted by H2, has symmetryU(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 gravitophoton, n0

gp denoted by Hermetry form H9 and represented by symmetry group SO(4), see Table2.

Hence, H8 allows the construction of a poly-metric, 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 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 two matter tables depict the classification scheme for physical interactions and particles as obtained from the

poly-metric 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. The only exception is the Hermetry form H16 for the Higgs field. 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 Higgs field (subspace R3 only) 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

cThere is of course a further aspect, namely the quantization of the associated metric fields that should result in the respective mediator bosons.

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R3 is associated with ordinary (real matter), see Tables 1-3. 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.

Table 1. Table of Hermetry forms for ordinary matter (OM) describing all messenger particles (gauge bosons), namely

graviton, photon, vector bosons, and gluons as well as all known types of matter (last three blue rows), i.e., leptons and

quarks. The gauge bosons comprise the four known fundamental forces. However, these forces are not sufficient to explain

the experiments by Tajmar et al. and Graham et al., as was shown in9 nor can they account for dark matter or dark energy.

The two additional gravitational fundamental forces are mediated by gravitophotons (attractive, n+

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 spacetime (vacuum field) and ordinary matter.

Any current of imaginary electrons or positrons can generate an imaginary vector potential, AI , that can interact

with imaginary charges to produce a real physical effect. These particles will eventually disappear, because of strict

charge conservation, and the resulting electromagnetic interaction is converted into a gravitational field. This

phenomenon might be the cause for the observed extremely strong gravitomagnetic and gravity-like fields in the

experiments by Tajmar et al.

The concept of imaginary matter in Table 2 should not be taken as if there existed a new type of 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.

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;m0; t0 have not been calculated, but 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. 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

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Table 2. Table of Hermetry forms for non-ordinary matter (NOM). First, it should be noted that 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 e

I together with its messenger particle gI . Second, the existence of neutral leptons is postulated.

Table 3. Hermetry form H16 stands for the Higgs field(s), which is the only Hermetry form that does not contain subspaces

S2 or I2 , emphasizing the special role of this field permeating all physical space.

Figure 3. Hermetry form H9 stands for the neutral gravitophoton, 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 acceleration field, the EHT experiment, see Sec. V. The second branch is assumed to occur in the

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

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comparing Tables 1 and 2, actually are the neutral leptons e0;m0; t0. At present, the mechanism of neutral lepton

production is not known, but, as is directly obvious from Table 1, the photon is the only particle that can be converted

into a gravitophoton n0

gp, which is the interaction boson for neutral leptons. It is therefore assumed that in the initial

phase of the Universe, when huge numbers of photons were present, these particles possibly could have formed. Since

they are not subject to electromagnetic interaction they might have life-times long enough to be stable and thus take

part in galaxy formation. Furthermore, the experiments by Tajmar et al. can be explained assuming the production of

gravitophotons by condensed matter phenomena, see Sec. IV, while accelerators are producing individual particles.

However, the production of neutral leptons does not seem to occur in gravitomagnetic experiments, but instead it is

assumed that NOM bosons occur in the form of gravitophotons and quintessence particles. In this regard, experiments

by Tajmar et al. represent a completely novel class of phenomena involving non-ordinary matter.

In order to construct the physically meaningful set of metric sub-tensors that is, Hermetryd 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.

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 poly-metric 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. 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,

each producing their independent spacetime curvature.

Having established the qualitative physical relationship between Hermetry forms and spacetime curvature, all physical

interactions are connected to spacetime curvature, similar to GR, and in this sense physics has been geometrized.

E. Symmetry Breaking Revisited

In order to find the force that might be used as the propellantless propulsion principle, the nature of the novel physical

interaction for the generation of gravitomagnetic fields needs to be determined. It is believed that the well known

effect of spontaneous symmetry breaking is responsible, requiring, however, a completely different approach.

A superconductor or a ferromagnet are models for spontaneous symmetry breaking, that is the potential energy of

the electron gas (superconductor) or the spin system (ferromagnet) changes abruptly at a critical temperature TC, and

the associated potential V(f) is changing its shape from the left to the right curve as depicted in Fig. 4. As a result, a

novel physical phenomenon occurs on the macroscopic scale.

For the subsequent discussion, the salient general characteristic features of symmetry breaking are listed below:

(i) Order parameter Spontaneous symmetry breaking is controlled by an order parameter, very often temperature.

At a certain critical temperature, a completely novel and unexpected behavior of the physical system appears.

(ii) New Particles Spontaneous symmetry breaking is associated with the formation of a new type of particles that

in, general, are strongly correlated. For instance, in superconductivity, Cooper pairs (two electron interaction,

boson like) are formed.

(iii) Novel Physical Phenomenon At the macroscopic scale a novel, completely different physical behavior occurs.

In superconductivity, electric resistivity becomes effectively zero at TC.

When symmetry breaking occurs, e.g. by reducing the temperature of the system, the potential curve changes

shape, moving from the left to the right picture in Fig. 4. The left shape is symmetric with respect to its single

minimum (at f = 0). For m2 < 0, the minima correspond to f = v. If spontaneous symmetry breaking sets in,

the field settles at one of these minima for the self-interaction has lowered the energy of the ground state (or vacuum

state). Thus the new shape (right picture) no longer reflects this symmetry, since the potential was shifted along the

abscissa by v. In other words, the symmetry has been broken spontaneously, i.e., by the physical system itself through

its self-interaction potential triggered by the critical temperature. The original vacuum state is no longer the correct

vacuum state, and the system has to assume a new vacuum state at f0 = v that is of lower energy. There is, however,

an alternative to this mechanism. Instead, the system decides to regain its symmetry and particles of imaginary mass

dHermetry stands for the physical meaning of geometry, combined from hermeneutics and geometry

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are generated. It is postulated that this is the mechanism of generating imaginary particles of real charge whose

subsequent conversion into gravitophotons is deemed to be responsible for the generation of the large observed

gravitomagnetic fields.

Figure 4. Symmetry Breaking Mechanism. The shape of the left potential function (depicted is ¤V on the ordinate, m2 and l have the

same sign) displays a unique ground-state (or vacuum state), which is defined as the state that possesses the lowest energy. This potential

belongs to a particle of mass m that is described by a Klein-Gordon field. At a critical temperature, TC, whose magnitude depends on

the physical system (e.g., superconductivity, superfluidity, ferromagnetism, condensed matter phenomena etc. ), so called spontaneous

symmetry breaking sets in.

F. Gravitomagnetism: Slight Symmetry Breaking and Particles of Imaginary Mass

It is surmised that spontaneous symmetry breaking is instrumental for the laboratory generated large gravitomagnetic

fields, since the magnitude of these fields suggests a coherent macroscopic phenomenon similar to superconductivity

or ferromagnetism.

The canonical symmetry breaking mechanism does not seem to be applicable, since eventually a gravitational

field is produced from a small rotating mass. Therefore, a different process than spontaneous symmetry breaking

should take place, termed gravitomagnetic symmetry breaking (GSB), since it needs to account for the mechanism

of first creating charged particles of imaginary mass from which the final gravitational field has to be produced. To

illustrate the difference between the conventional symmetry breaking e and GSB, we consider a scalar field that occurs,

for instance, in ferromagnetism. It describes the potential energy of the spin system formed by the individual atoms.

Replacing classical coordinates qi by scalar fields f gives the general formulation of the Lagrangian

L = ¶mf¶ mf ¤V(f) with V(f) = ¤

m2f2¤

f4: (3)

fThe first term of the Lagrangian describes kinetic energy, the second term the potential energy (harmonic oscillator) g,

and the third term stands for the self-interaction energy that physical systems exhibit in case of spontaneous symmetry

breaking, i.e. the sign of l changes from positive to neagtive, see Fig.4. In the case of ferromagnetism, the field

variable f is replaced by magnetization M . Here, the coefficient of M4 in potential V(f) changes sign from minus to

eFor an excellent detailed introduction to this highly important phenomenon see Kaku,19 and also Schmüser,20 Zee,21 or Lahiri22 as well as the

article by Scheck23 .

f There are no third order terms f3, since V(f) is invariant under the transformation f !¤f:

gThe so called Higgs field, represented by the symmetric Lagrangian as given above, would satisfy the Klein-Gordon equation, (+m2)f(x) =

0; which describes a scalar particle of mass m, i.e., a particle with one Lorentz invariant, namely its four momentum pm pm = mc2. For a particle

with charge q, function f(x) =

(f1(x)+if2(x)) has to be chosen complex. In the ground state jf0j the associated Noether current is given by

jm = ¤2q2jf0j2Am . In case the electromagnetic interaction is associated with the symmetry breaking, the vector potential, Am , hitherto represented

by the massless photon, g, must have acquired the real mass M =

2qjf0j20 . Thus, spontaneous symmetry breaking has the capability to provide

real physical mass to a former massless particle.

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plus at T = TC, the Curie temperature, and thus the potential changes its shape, namely from the left to the right curve

in Fig.4. Hence, V(f) assumes a new minimum (negative) at M0 (or f = f0). The field is interacting with itself, which

means for the superconducting state that the wave functions of the individual Cooper pairs are strongly correlated,

forming a single macroscopic wave with y2C

P = n where index CP denotes Cooper pairs and n is their spatial density.

In a ferromagnet there exists an interaction among the magnetic moments of the electrons of the 3d-orbits that are not

closed.

For the explanation of spontaneous symmetry breaking according to quantum field theory (QFT) it is argued that

the physical system is moving away from its original vacuum state (left curve in Fig. 4 and moves down the potential

curve (right curve of Fig. 4) to the bottom of one of the wells to achieving a lower energy state. Consequently,

the conventional interpretation of spontaneous symmetry breaking starts a Taylor expansion about the new minimum

located at f0 =

¤6m2=l, see also19 . This means that a new field f˜ := f ¤f0 is defined that now assumes its

minimum at f˜ = 0. Now the potential expressed in terms of f˜ has the form

V(f˜) = ¤

m2f˜2+

lf0 f˜3+

f˜4

which means that the origin of the coordinate system was shifted to the new vacuum and therefore the potential is

no longer symmetric under the transformation f˜ !¤f˜. Thus, the symmetry was spontaneously broken. In addition,

as is mentioned in the footnote below, a novel particle of real mass mass has been created. So far the conventional

interpretation of the role of spontaneous symmetry breaking.

Next, we present the spontaneous symmetry breaking mechanism, as suggested by EHT, considered responsible

for the generation of the Bgp field. In order to explain the existence of these strong gravitomagnetic fields, the above

mechanism does not work since electromagnetism is not the only interaction involved. Eventually, a gravitomagnetic

field is measured. If we now suppose that in the Lagrangian, Eq.3, m2 were negative, the new minimum of potential V

is given by f0 =

¤6m2=l and the expectation values of the vacuum state is not zero, but is given by

h0jfj0i = f0: (4)

In the literature this potential is sometimes called the tachyon potential. If m2 is negative, then m is imaginary. The

conventional interpretation is that the theory predicts particles of imaginary mass, moving at superluminal speed,

called tachyons. Tachyons, however, have never been observed despite substantial experimental efforts. Quantum

mechanically, one reinterprets the theory to mean that one has simply expanded around the wrong vacuum and the

symmetry appears to be broken.

The salient characteristic features of GSB (Gravitomagnetic Symmetry Breaking) are stated below. Its application

to the gravitational experiments (Sec. III) is detailed in Sec. IV. In order to explain GSB the two novel physical

concepts derived from the Hermetry picture are utilized, namely the existence of three gravitational forces (Fig.2)

and the existence of non-ordinary matter (Table 2)h.

(i) GSB Order parameter GSB symmetry breaking is controlled by temperature. At a certain critical temperature,

denoted TB, the cryogenic material exhibits a totally unexpected behavior such that extreme Bgp fields are

produced. For instance, in the experiments at ARC a value of TB = 15:9K was found for the cryogenic rotating

Nb ring.

(ii) GSB New Particles GSB symmetry breaking is associated with the formation of virtual electrons, eI and protons,

pI of imaginary mass (in the form of imaginary quarks), generated by the GSB mechanism. These particles

belong to NOM, see Table 2, and do not exist in the current framework of ordinary matter given in Table 1.

(iii) GSB Novel Physical Phenomenon On the macroscopic scale, the novel physical behavior is manifesting itself

in the form of extreme Bgp fields.

G. Energy and Momentum Conservation Revisited

Relativistic space flight is not an option, since any space vehicle attaining velocities close to the speed of light can

only achieve this at the expense of an infinite amount of energy, if the theory of special relativity (SR) was governing

all physical laws. i

hThe following explanations are merely attempting to proposing the physical mechanism for the generation of the measured gravitomagnetic

field. The mathematical analysis of this mechanism will have to demonstrate its viability.

iSR is experimentally very well established and thus is a validated physical theory. However, this does not exclude the existence of additional

physical interactions as suggested by the gravitomagnetic experiments. Second, the range of applicability of SR is Minkowski space M4, i.e., there

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Even if nonrelativistic flight of a spacecraft of mass 105 kg at a speed of 104 km/s is considered, the kinetic energy

to be provided is 51018 J. A 100 MW nuclear reactor, providing the power for this spacecraft, would need 51010

s or about 1,500 years to produce this amount of energy. This scenario is somewhat unrealistic, since the mass of the

reactor was not accounted for. Clearly, physical laws governing this type of space propulsion are not suitable for real

space travel.

Therefore, as an alternative means to space propulsion, already in 1960 Corliss2 investigated the use of natural

force fields, focusing on propulsion systems that do not rely on the expulsion of mass and energy. In other words,

Corliss already discussed a propellantless propulsion mechanism. However, his discussion was restricted to conventional

gravitational, magnetic (e.g., using the Earth magnetic field for propulsion), and electric (nothing has been

observed) fields in space. He also discussed the modification of gravity, but Tajmar et al.24 have already shown that

even if modified gravitational laws existed, their usage for space propulsion is negligible. The conclusion reached

by Corliss was that nothing has been uncovered to allow any action-at a-distance force field for space propulsion in

interplanetary or interstellar space.

Concerning the production mechanism of gravitophotons, as long as T < TC, gravitophotons will be produced by

the mechanism described in Sec. IV, and a strong Bg field is observed. As discussed in Sec. III C, there is evidence

from ARC experiments that the temporal variation of this field leads to a gravity-like (acceleration) field and thus to

a novel force. The important fact is that in the generation of this force through the decay of the gravitophoton both

particles from OM (graviton positive energy density) and NOM (quintessence particle, negative energy density). The

total energy needed in generation these two particles is therefore zero. Gravitons interact with the space vehicle and

cause its acceleration while the momentum of the quintessence particle is not felt by the space vehicle but by the

surrounding spacetime.

III. Experiments for the Laboratory Generated of Gravitational Fields

In this section, we are dealing with gravitational fields that are gravitomagnetic (1/s) or gravity-like (acceleration,

m2=s) fields, generated in the laboratory by a cryogenic rotating mass below a certain critical temperature. In

comparison to GR, these gravitomagnetic fields are about 18 orders of magnitude larger than those predicted by the

frame dragging effect of GR. Therefore, if current experiments are confirmed, the physics of these fields must be

outside GR. The physical mechanism underlying this effect, according to EHT, will be discussed further in Sec. IV. It

was, however, shown in9 that, if experimental measurements are correct, none of the currently known four physical

interactions would be sufficient to account for these novel physical phenomena.

A. Present Experimental Basis for Gravitational Fields

Recently Tajmar et al. carried out a comprehensive series of different gravitomagnetic experiments33 termed A, B, and

C. The difference between the three experimental setups is as follows.

Setup A In setup A the sensor vacuum chamber is directly above the cryogenic spinning ring. There is a very thin

sheet of insulating material, MLI j, between the vacuum chamber and the sample holder containing the rotating

ring. However, there is no MLI between the upper surface of the ring and the sensor vacuum chamber.

Setup B In setup B the vacuum sensor chamber is inserted in a stainless steel container, and thus the gyroscope could

be shielded to some extent from the gravitomagnetic field of the rotating ring.

Setup C In experiment C, the stainless steel shielding of Setup B is replaced by an MLI made container of about 1

cm thickness.

Canterbury Experiment In the experiments by Graham et al. a large laser ring gyro is used, and the resulting

gravitomagnetic field is measured outside the vacuum sensor chamber. However, the sensitivity of this laser

gyro was two orders of magnitude lower compared to the gyro used in Setup B and C.

is no acceleration of the space vehicle. This does not necessarily exclude the existence of other physical spaces, which a space vehicle might be able

to enter and leave under certain physical conditions. Third, spacetime is discrete (quantized version of spacetime), and as such cannot be Lorentz

invariant.

jMulti Layer Insulation, responsible for the gold foil color in spacecraft insulation, is used for thermal insulation in vacuum by minimizing

radiation losses. A single layer has a thickness of approximately 10¤5 m. It is made from amber colored Kapton (plastic), having on one side a

silvery aluminum coating for high thermal reflection in the infrared. Other material combinations like Mylar (plastic) and silver are also used.

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Gravity-Probe B Gravity-like fields might have been observed also in the NASA-Stanford Gravity Probe B Experiment

and were already discussed in9 . According to EHT, part of the observed gyro anomaly should be due

to the existence of gravity-like fields, and should not be completely explainable by electrostatic forces (patch

effect).

B. Gravitomagnetic Field Experiments at Austrian Research Centers

The experimental setups A, B, and C have resulted in highly varying gravitomagnetic field strengths as can be seen

from Tables 4 , 5. There are several points to be noted.

In Setup A, the evaporating helium escapes through the duct on the upper left hand side and gaseous helium,

produced by evaporation of the liquid helium from the cyrostat, is streaming along the walls of the stainless steel

vacuum sensor chamber housing the gyros. The shaft, see middle axis, is a massive stainless steel rod of 20 mm

radius or, as used in the most recent experiments,33 was replaced by a tubular structure, in order to strengthen the gyro

support. There is an MLI layer, (thin Al foils), half the thickness of the one employed in Setup C, insulating the sample

holder from the vacuum sensor chamber. There is no MLI material in the gap directly above the ring and the sensor

chamber. The measurements from this Setup are shown in Table 4. The gyros are housed in a 2 mm strong stainless

steel casing. The gyro support is an Al plate of thickness 2-3 mm.

In Setup B the sensor chamber is embedded in a steel vessel so that ring and chamber are further separated by a 5

mm distance. Thus the contact of the evaporating helium with the sensor chamber is reduced. However, some liquid

helium is vented through openings (not visible in the left figure) in the flanges connecting the cryostat and insulation

vessel, in order to prevent ice formation along the sensor chamber walls. The velocity of this helium gas should be

small, since it passed through the stack of cooling metal sheets. The major part of evaporating helium leaves the

cryostat through the helium venting tube on the upper left. Here, a single, but substantially more sensitive gyro is

used. This gyro has a larger footprint than the ones in Setup A.

In Setup C the evaporating helium stream does not stream along the sides of the vacuum sensor chamber. Compared

to experiment B, the gyro chamber is thermally insulated from the helium by an additional layer of MLI. The shaft, see

middle axis, is a tubular structure. Gaseous helium, produced by evaporation of the liquid helium from the cyrostat,

is now streaming along the sides of the inset cryostat, made from MLI, which replaces the insulating stainless steel

chamber of setup B. The measurements from these two variants are shown in Table 4. The gyro support is an Al plate

of thickness 2-3 mm. The liquid helium in the cryostat does not take part in the rotation, since the filling level in

general remains below the sample holder, except for the results shown in the first yellow row of Table 5.

Comparing the gyro results as shown in Table 4, it is obvious that there are substantial differences in the clockwise

gyro signals, and it also might seem that there are inconsistencies in the measured counter-clockwise signals. However,

as shown in the rightmost column, the ratio of the CW/CCW signals, within their specified measured uncertainties,

always assumes one of the integer values 1, -1, 5, and -5 as predicted in. At present, it cannot be predicted under

which experimental conditions a specific ratio is seen. These values should occur according to EHT, and are derived

considering the partial terms of the corresponding Hermetry forms. The last row (green) shows the results by Graham

et al.32 . Results of Graham were obtained by utilizing the high precision ring laser gyro UG2, operated by the

Canterbury Ring Laser Group that has dimensions 21.0 m 39.9 m. In this experiment, due to its size, the gyro is

operated outside the cryostat, and therefore any influence of evaporating helium on gyro vibrations can be excluded.

The change in sign (compared to results of Tajmar et al.) of the Bg field can directly be explained from the fact that the

ring laser gyro saw the downward component of the dipole gravitomagnetic field component, since the measurement

location was outside the disk.

In setups B and C the angular frequency was limited to w = 100rad=s instead of w = 420rad=s in setup A (see

Table 4). Comparing the results of setups B and C, it is obvious that there is substantial difference in the magnitude

of the gyro signals. Furthermore, if the 5s rule is employed that, in order to have a valid gyro signal, the measured

signal magnitude must be at least five larger than the standard deviation, only the measured results of the first red

row would qualify as a valid signal. In addition, even the CCW value in this row might have to be considered a null

signal. From33 all uncertainties are restricted to one digit accuracy, no information is available on the second digit.

Applying the same rule to the yellow measurements, all measured results should be disqualified, except perhaps the

first value in the first row. However, if the uncertainty were about 10 % larger than specified, this result also would

have to be considered a null result. Since the uncertainties in setup C are already one order of magnitude less than the

ones in setup B, it is not clear how accurate they were determined. In other words, it could be that all results in setup

B and C need to be discarded. There seems to be substantial uncertainty to interpret the signals of setup C in such a

way that only the rotating liquid helium is giving a signal, while the gravitomagnetic signals of the Al-Al and Nb-Al

are counted as null. If the casing of setup C works similar to a gravitomagnetic cage, all signals are being drastically

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Table 4. The three (yellow) rows depict the measured values for Setup A, compiled from30 .The following four (red) rows show the gravitomagnetic

field measurements (shown is the so called coupling factor 108 at temperatures T = 4¤6 K, that is defined as gyro-signal

per angular frequency (rad s¤1=w) for Setup A as reported in Tajmar et al.33 . The last row, green, shows the measurements obtained

from Graham et al. where a disk was used and measurements were done outside the cryostat employing a large ring laser. Note that these

measurements do not satisfy the 5 s rule. Measured magnitudes of the Bg depend on the direction of rotation. The last column shows the

theoretically calculated ratio.

reduced. However, as shown again in the rightmost column, the ratio of the CW/CCW signals, within their specified

measured uncertainties, seems to assume one of the integer values 1, -1, 5, and -5 as already mentioned in Table 4 .

Assessment of Gravitomagnetic Field Experiments:

• The measured CCW signals for Setup A in Table 4 reveal a change in sign.

• The noise levels in Setup A are in the range of the largest signal measured in Setup C.

• If the 5 s rule is strictly applied, the results in Table 5 would have to be discarded and the same holds for several

measurements of Table 4.

• On the other hand, the gyros report sign changes in the signals, i.e. they actually seem to see a signal, which is

no random.

C. Gravity-Like Field Experiments at Austrian Research Centers

In these experiments a gravitomagnetic force is produced by a ring, disk or sphere that needs to be accelerated or

decelerated in order to obtain a gravity-like field in the rotational plane directed in the circumferential direction. The

gravity-like field acts against the original mechanical acceleration or deceleration field. This experiment, if confirmed,

would have seen a novel physical force. Application to a novel technology, however, is not at all straightforward. First,

the process of acceleration or deceleration can only be sustained for a very limited period of time. Any acceleration

eventually must be followed by a deceleration, so that over a large enough averaging period in time the gravity-like

field is zero. Second, the field is in the circumferential direction, making it difficult to use it as propulsion source.

IV. Physical Mechanism of Gravitational Experiments

As was shown in9, 12 the neutral gravitophoton that causes the gravitomagnetic force can decay into a graviton

and quintessence particle, as is assumed to be the case in the ARC and Graham experiments as well as for GP-B.

There should, however, exist a second decay avenue, namely into a positive (repulsive) gravitophoton and negative

(attractive) gravitophoton , which should take place in the proposed experiment for the axial acceleration field (Fig.

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Table 5. The three (red) rows show the coupling factor 108 at temperatures T = 4¤6 K for Setup B and C as reported in Tajmar et al.33 .

The following three (yellow) rows depict the measured values for Setup C, compiled from30 . The green row shows measured results at the

temperature of liquid nitrogen. Since the effect is associated with a phase transition at low cryogenic temperatures a zero gravitomagnetic

field is to be expected.

6). In the experiment by Tajmar et al. the gravity-like field k is in the circumferential direction and needs a time varying

neutral gravitophoton field, see9 . For the axial field generation, the time varying differential operator is replaced by

a spatially varying operator, which should lead to a completely different nature of the gravity-like force that is much

more amenable to space propulsion purposes, since it should be directed along the axis of rotation.

In both cases the energy extracted from the vacuum is zero, since graviton and quintessence particles have positive

and negative energy densities, respectively. If only the energy of the gravitons were 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 negative energy density of the quintessence particle was not accounted for. In the axial field experiment, 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. The important role of the vacuum field is (spacetime) that it allows this type of pair creation. It

seems to act as catalyst for such a reaction.

First, the list of particles is given that might be involved or being created during the physical processes that are

taking place in the generation of gravitomagnetic or gravity-like fields.

(i) e the electron is assumed to carry a negative charge,

(ii) p = uud proton from crystal lattice comprising three quarks (u has charge +2=3e and d quark ¤1=3e),

(iii) ng graviton,

(iv) eI imaginary electron, same charge as the electron,

(v) qI three imaginary quarks generated within protons of the crystal lattice at cryogenic temperature together eI

satisfying charge conservation,

(vi) nq quintessence particle,

(vii) eBI

:=eI+eI imaginary electron-boson pair from two electron interaction, which is similar to eB :=e+e electronboson

pair. According to experiment, the gravitomagnetic field was already measured at temperatures around

25 K, somewhat above the critical temperature of Nb (9.2 K), and hence eB pairs might not be needed,

(viii) n0

gp !ng+nq, neutral gravitophoton generated in the gravitomagnetic experiments by Tajmar et al.,

kThe experiments by Tajmar et al. and Graham et al. are also discussed by Hathaway, Chap. 5, in3 . Data from the two experiments show

similarities, in particular, a signal strength dependence on the direction of rotation, though measurement techniques were completely different. One

of the conclusions is that further independent experiments need to be performed.

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(ix) n0

gp !n+

gp+n¤

gp, neutral gravitophoton generated in vertical gravity-like field as proposed from EHT.

Second, in all experiments generating gravitomagnetic or gravitoelectric (acceleration) fields the production of

imaginary matter is assumed, whose subsequent conversion into a gravitomagnetic or gravitoelectric field is

deemed responsible for the enormous frame dragging like effect, which is about 18 orders of magnitude larger than

that of GR and therefore outside GR. The production mechanism for imaginary matter (PIM) is supposed to proceed

in the following stages:

1. PIM [ qI generation in Nb ring ] at a critical cryogenic temperature (material dependent), a phase transition

occurs and imaginary quarks qI within the protons of the crystal lattice are produced. The three qI quarks are

the source of an imaginary vector potential AI . Neutrons do not contribute to eI generation, since they do not

carry charge,

2. PIM [ eI generation in Nb ring ] at the same time imaginary electrons are produced, according to the mechanism

of symmetry breaking, described in Section. II E, and are supposed to appear as free imaginary electron gas,

3. PIM [ eBI

generation in Nb ring ] imaginary electron-boson pairs may be formed as in conventional BCS theory,

due to the exchange of lattice vibrations, also known of phonons. l

Third, three different types of gravitational experiments are discerned in the generation of the gravitomagnetic or

gravitoelectric fields. The different options are listed below:

1. [Gravitational Experiment 1: Gravitomagnetic field] Rotating the cryogenic Nb ring at constant angular

velocity wNb produces a gravitomagnetic field Bgp only. This field was measured by Tajmar et al. and Graham

et al., causing a rotation (twisting) of spacetime, and also seems to (partially) cause a misalignment of the gyro

axes in the GP-B experiment. No acceleration field is present.

2. [Gravitational Experiment 2: horizontal acceleration field ] Using a mechanical force to accelerate the

cryogenic Nb ring that is, variation of wNb, generates a tangential (or circumferential) gravity-like (acceleration)

field ggp located in the plane of the ring in circumferential direction, acting against its origin (i.e., the mechanical

acceleration), following some kind of Lenz rule, as measured by Tajmar et al.

3. [Gravitational Experiment 3: vertical acceleration field] Employing a (special material) superconducting

solenoid to induce a magnetic induction field in the cryogenic (superconducting) ring (or disk) should generate

a vertical gravity-like acceleration field (GE 3, see Fig 6) acting along the axis of rotation of the Nb ring (or

disk), predicted by EHT. In this experiment the ring (or disk) is rotating at constant speed, in contrast to GE 2.

Fourth, there seem to exist two coupling mechanisms to generate gravity-like fields, termed fermion and boson

coupling.

Fermion coupling: Imaginary charges are created by radiation coupling in form of virtual electron-positron pairs and

their interaction with the complex Higgs field38 . This type of coupling requires very strong magnetic induction

fields, and thus is no longer pursued.

Boson coupling: Experiments of Tajmar et al.29–31 . Imaginary electron pairs (boson like) eBI

(Hermetry form

H11(T1 S2)), possibly created by some kind of two-electron interaction (similar to conventional BCS theory),

are interacting with the imaginary vector potential AI from the imaginary quarks qI in the lattice, resulting

in real physical interaction. The technical requirements for achieving boson coupling are less demanding than

for fermion coupling. For instance, the strength of magnetic induction field is substantially lower for boson

coupling.

Fifth, the description of the physical processes that are taking place in the generation of gravitomagnetic and

gravitoelectric fields are presented. In a step by step fashion, the sequence of physical phenomena as they occur in the

various stages of the experiments are presented.

lIt is however assumed that there is no interaction between charged real and imaginary particles that is, the generic many-particle Hamiltonian

for a metal H = He +Hi +Hei is not modified by the presence of terms like HeeI or HieI , but a term HeI eI might be added.

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1. Cryogenic temperature Nb-ring: In all experiments, the rotating Nb ring is cooled down to cryogenic temperatures.

Gravitomagnetic or gravity-like fields are observed only below a certain critical temperature, TG, which is

generally higher than the critical temperature, TS, for superconductivity. Therefore, the mechanism that triggers

the onset of gravitomagnetic fields, has to be associated with its proper phase transition where temperature is

the order parameter.

2. Constant rotation of Nb ring and Al sh: In Experiment 1, both the Al sample holder (sh) and its sample, namely

the Nb ring that is mechanically fixed to the Al sh, are rotated at constant angular speed wNb. It is known that,

reaching a critical temperature, TG, spontaneous symmetry breaking occurs, and the cryogenic material (i.e., Nb

ring, Al sh, and also the liquid He itself ) will be in the gravitomagnetic state as denoting this kind of phase

transition. As it seems, the superconductive state is not necessary for the gravitomagnetic state, but perhaps it is

a sufficient condition, at least for some materials.

3. Cryogenic temperature Al-sample holder: Superconductivity comprises two-electron interactions that is, producing

electron-boson (Cooper) pairs, eB, as described under 3. PIM. The gravitomagnetic state is similar, such

that by employing 2. PIM, imaginary electron-boson pairs, eBI

, are generated. In agreement with 1. PIM, imaginary

quarks, qI , are generated by the protons in the crystal lattice in the Nb ring that are fixed to their locations

of origin. According to 2. PIM, imaginary electron pairs eBI

are also generated in the Al sample holder.

4. Conversion from electromagnetic to gravitomagnetic field : The imaginary electron pairs that are moving with

the crystal lattices of the rotating Nb ring and Al sh, interact with the imaginary vector potential, AI , from the

stationary imaginary quarks. The interaction of these virtual imaginary particles causes a real physical effect,

namely, since no electromagnetic effect is observed, instead conversion into a gravitomagnetic field must have

taken place by the production of neutral gravitophotons n0

gp, which are considered to be the field quanta of the

observed gravitomagnetic field Bgp.

BCW

gp = 20p 1

pagp

rAwNb (5)

where r is the combined density of Nb ring (8:57103 kg/m3) and Al sample holder (2:70103 kg/m3) and

A = 2p 7:510¤2 610¤3 = 2:8310¤3m2 is the area of the ring, see Fig. 5. For the actual magnitude

of the Bgp field the masses of the ring and sample holder (and thus the distribution of mass) is of importance as

well as the material. The field scales linearly with the angular velocity wNb of the ring, at least over a certain

range of wNb.

V. Gravitational Space Propulsion Device

In GME 1 and 2 that are specifically designed for the generation of gravity-like fields, the gravitational force

is acting in the plane of rotation in circumferential direction, opposing the original acceleration of the ring or disk,

following some kind of Lenz rule. The same holds true for GME 3, 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 along the axis of rotation, while the speed of rotation remains constant. The existence of

such a field is based on the fact that spatial and temporal coordinates should be of the same physical quality.

Considering the experimental setup by Tajmar et al. that comprises an aluminum (Al) sample holder (the Nb

ring) and cryogenic rotating Nb ring fixed to the sample holder, and thus rotating at the same angular velocity. Two

acceleration components are generated: one in the radial r direction of the disk, and the second one in the z- direction.

The first one, has to be absorbed by the structure of the configuration, thus creating a mechanical load. The component

in the z-direction, responsible for the acceleration field, is given by

Bg;z = k kNb kAl

wI ; az ˆez =

Bg;z(ˆeq ˆez)ˆeq (6)

and wI is the angular velocity of the imaginary electron pairs, vsh denotes the mechanical velocity of the rotating

sample holder, and Bg;z is the component of the gravitophoton field Bg (dimension 1/s) in the z-direction. It should

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Figure 5. The picture shows the Nb ring as utilized in the experiments by Tajmar et al.

be noted that the magnitude of the gravitomagnetic field Bg does not depend on the mechanical angular velocity at

which Al sample holder and Nb ring are moving. In contrast to Fermion coupling, ref.,38 experimental requirements

are substantially lower.

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 13:6A (needed to calculate Bz), diameter of solenoid 0:15 m, and vTq =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 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 1:98106N, a mass of 3:15103kg and

a rotation speed of 200 m=s, a coil of 1 m diameter with 2,500 turns and a current of 13:6 A was calculated. The

cross section area of the coil was determined to be about 2:510¤2 m2. These numbers will be recomputed in our

forthcoming review article. All trip times given in38 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.

VI. 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 interactions9, 13, 14 . 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. at ARC 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 100 grams utilized by Tajmar, produces a frame

dragging effect similar to the mass of a white dwarf9 . These experiments were repeated by Graham et al.32 in 2007,

and more recently Tajmar et al.31 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

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Figure 6. 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).

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

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

temperature for superconducting, but possibly boson interaction took place (virtual imaginary particles). GR cannot be

used to explain these phenomena, even if the full nonlinear Einstein field equations were used. The Lageos and GP-B

experiments have clearly demonstrated that the inertial frame dragging effect, even from celestial bodies, is extremely

small and within GR. These facts provide evidence for novel physics in the form of additional long range fundamental

forces.

How to proceed? The experiments performed so far, if confirmed, will serve as demonstrators for the existence of a

novel physical effect. However, in order to produce a propellantless space propulsion system, the experiment of Sec.

II 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, an axial field might directly lead to

some kind of gravity control.

Furthermore, gravity-like fields most likely would lead to novel technologies in the general field of transportation,

and thus should be of major interest to the public and, in particular, to industry. In addition, these fields might also be

usable in energy generation leading to energy research that is highly relevant to the future.

VII. Acknowledgment

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, ARC 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 für Grenzgebiete derWissenschaft

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

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