AIAA 2006-4608 SPACETIME PHYSICS AND ADVANCED PROPULSION CONCEPTS Revised Extended Version (20 Agust 2006)

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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

1. Villard, R., L.R. Cook, Infinite Worlds, Univ. of 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., 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

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