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Page 1

Heim Quantum Theory for Space Propulsion Physics

Walter Dröscher

1

, Jochem Häuser

1,2

1

Institut für Grenzgebiete der Wissenschaft (IGW),

Leopold - Franzens Universität Innsbruck, Maximilianstr. 8, 6010 Innsbruck, Austria

2

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

contact: e-mail: jh@cle.de

Abstract. This paper describes a novel space propulsion technique, based on an extension of a unified field theory in

a quantized, higher-dimensional space, developed by the late B. Heim (1977) in the 50s and 60s of the last century,

termed Heim Quantum Theory (HQT). As a consequence of the unification, HQT predicts six fundamental

interactions. The two additional interactions should enable a completely different type of propulsion, denoted

gravitophoton field propulsion. The fifth interaction, termed gravitophoton force, would accelerate a material body

without the need of propellant. Gravitophoton interaction is a gravitational like force, mediated by gravitophoton

particles that come in both types, attractive and repulsive. Gravitophoton particles are generated in pairs from the

vacuum itself by the effect of vacuum polarization (virtual electrons), under the presence of a very strong magnetic

field (photons). Due to gravitophoton pair production, the total energy extracted from the vacuum is zero. Attractive

gravitophotons interact with matter, and thus can become real particles, exacting a force on a material body.

Repulsive gravitophotons have a much smaller cross section and do not interact with matter. Consequently, the

kinetic energy of the accelerated material body would come from the vacuum, satisfying the second condition, i.e., a

low energy budget for space propulsion. The name gravitophoton has been chosen because a transformation of

photons into gravitational energy should take place. The third condition for advanced spaceflight, superluminal

speed, may be realized by transition into a parallel space, in which covariant laws of physics are valid, with a

limiting speed of light nc, where n is an integer and c is the vacuum speed of light. In order to achieve such a

transition, the sixth fundamental interaction would be needed, termed vacuum field (or quintessence), which is a

weakly repulsive gravitational like force, mediated by the vacuum particle, being formed by the interaction of

repulsive gravitophotons with the gravitons of the spacecraft. The paper discusses the source of the two predicted

interactions, the concept of parallel space, and presents the physical model along with an experimental setup to

measure and estimate the gravitophoton force. Estimates for the magnitude of magnetic fields are presented, and trip

times for lunar and Mars missions are given.

SPACETIME AND SPACE PROPULSION

For effective and efficient lunar space transportation as well as interplanetary or interstellar space flight a

revolution in space propulsion technology is needed. In this paper the physical principles for a novel propulsion

scheme are presented, obtained from an extension of HQT (Heim, 1977). According to HQT, the goals of NASA's

Breakthrough Propulsion Physics Program (BPPP) (Millis, 2004) may be satisfied. It should be expected that new

physics leads to completely new technology (Thiemann, 2002). The requirements of BPPP for revolutionary space

propulsion are that no or a very limited amount of fuel is used, a low energy budget is maintained, and (possibly)

superluminal speed is reached. This immediately rules out any device flying today, or any concept that accelerates

a vehicle close to the speed of light. A spacecraft moving only at a small fraction at the speed of light would

require a tremendous energy input, rendering such an attempt impractical.

Physical Concepts of HQT

It is known that the general theory of relativity (GR) in a 4-dimensional spacetime delivers one possible physical

---

Page 2

interaction, namely gravitation. Since Nature shows us that there exist additional interactions (EM, weak, strong),

and because both GR and the quantum principle are experimentally verified, it seems logical to extend the

geometrical principle to a discrete, higher-dimensional space. Furthermore, the spontaneous order that has been

observed in the universe is opposite to the laws of thermodynamics, predicting the increase of disorder or greater

entropy (Strogatz 2003). Everywhere highly evolved structures can be seen, which is an enigma for the science of

today. Consequently, the theory utilizes an entelechial dimension, x

5

, an aeonic dimension, x

6

(see glossary), and

coordinates x

7

, x

8

describing information, i.e., quantum mechanics, resulting in an 8-dimensional discrete space in

which a smallest elemental surface, the so-called metron, exists.

Poly-Metric and the Fundamental Physical Interactions in 8-D Quantized Heim Space

In GR the gravitational force is nothing but an effect of the geometric curvature of spacetime. The predictions of

GR have been tested extensively. Therefore, there is some confidence that this concept can be extended to all

physical forces, and that the structure of the equations of GR is valid for all physical interactions in a higher-

dimensional space, termed the Einsteinian Geometrization Principle (EGP). There are the subspaces ℝ

3

with real

coordinates (x

1

, x

2

, x

3

) that is + signature (Carroll 2004), T

1

with the – signature time coordinate (x

4

) , S

2

with -

signature coordinates for organization of structures (x

5

, x

6

), and I

2

with -signature coordinates for information (x

7

,

x

8

). In the following, a Heim space is a quantized space comprising elemental surfaces with orientation (spin), the

metron, whose size is the Planck length (apart from a factor) squared, comprising 6 or 8 dimensions. A Heim space

may comprise several subspaces, each equipped with its own special metric, whose signature is derived from the

signature of the individual subspaces. It should be remembered that the Lorentzian metric of ℝ

4

has three spatial (+

signature) and one time-like coordinate (- signature) (Carroll 2004). Heim space H

8

, where the superscript denotes

dimension, comprises four subspaces or partial structures that form semantic units. Combining these semantic

units by employing certain selection rules, a set of so called hermetry forms or partial metric tensors is obtained,

forming a poly-metric that represents all known physical interactions. Considering the space H

8

= ℝ

3

∪T

1

∪S

2

∪I

2

,

the theory predicts six fundamental interactions, instead of the four experimentally known ones. These interactions

emerge in our spacetime and represent real physical fields carrying energy. According to the theory, a

transformation of photons into gravitational energy (gravitophoton) should be possible. It is this conversion that is

used as the physical basis for the novel space propulsion concept. This is a direct consequence of Heim space, and

the interpretation of a partial metric (hermetry form, see glossary) as a physical interaction or particle.

Six Fundamental Interactions in HQT

The two additional interactions predicted in HQT are identified as gravitophoton interaction, enabling the

conversion of photons into a gravitational like field, represented by two hypothetical gravitophoton (attractive and

repulsive) particles and quintessence, a weak repulsive gravitational like interaction (dark energy). The

interpretation of the physical equations for the gravitophoton field leads to the conclusion that this field could be

used to both accelerate a material body and to cause a transition of a material body into some kind of parallel

space, possibly allowing superluminal speed. According to Heim's theory, gravitation, as we know it, is comprised

of three interactions, namely by gravitons, gravitophotons (attractive and repulsive), and by the quintessence or

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

constant G contains contributions from all three fields. The quintessence interaction, however, is much smaller

than the first two contributions. Furthermore, in GR the gravitational potential is associated with the metric

tensor, and thus has a direct physical meaning. In other words, if the EGP is extended to the poly-metric in Heim

space H

8

, the existence of exactly six physical interactions occurs as a natural consequence.

PHYSICAL PRINCIPLES OF GRAVITOPHOTON FIELD PROPULSION

In GR the metric has the meaning as physical potential for gravitation. As was mentioned before this view is

extended to Heim space H

8

. We now present the most general transformation that is responsible for all physical

interactions. Most important is the double transformation as described in Eq. (1). A curve in ℝ

4

can be specified

by either Cartesian coordinates

x

m

or by curvilinear coordinates

i

.

However, since ℝ

4

is a subspace of Heim

---

Page 3

space H

8

with so called internal coordinates

(Dröscher and Hauser, 2004), there exists a general coordinate

transformation

x

m

i

from ℝ

4

H

8

ℝ

4

resulting in the metric tensor (this is a major difference to GR)

g

i k

=

∂ x

m

∂

∂

∂

i

∂ x

m

∂

∂

∂

k

,

g

i k

=:

∑

, =1

8

g

i k

,

g

i k

=

∂ x

m

∂

∂

∂

i

∂ x

m

∂

∂

∂

k

.

(1)

where indices α, β = 1,...,8 and i, m, k = 1,...,4. The Einstein summation convention is used. The above

transformation is instrumental for the construction of the poly-metric utilized to describing all possible physical

interactions. The metric tensor can be written in the form as expressed in the second term of Eq. (1). Parentheses

indicate that there is no index summation. In Dröscher and Hauser (2004) it was shown that 12 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 H

ℓ

with ℓ=1,...,12 is used:

g

i k

H

ℓ

=:

∑

, ∈H

ℓ

g

i k

(2)

where summation indices are obtained from the definition of the hermetry forms. The expressions

g

i k

H

ℓ

are

interpreted as different physical interaction potentials caused by hermetry form H

ℓ

, extending the interpretation of

metric employed in GR to the poly-metric of H

8

. Next, the hermetry forms pertaining to the three subspaces S

2

,

I

2

, S

2

× I

2

are investigated. Cosmological data clearly show that the universe is expanding, which indicates a

repulsive interaction. Gravitational attraction is well known since Newton. Both interactions act on matter, so that

there should be two hermetry forms having anti-symmetric properties. The spaces corresponding to these

interaction are identified as S

2

and I

2

. For the sake of simplicity, the following short form, omitting subscripts ik, is

introduced

:=g

i k

.

The gravitational field, as described by gravitons, is given by hermetry form H

12

, and

the vacuum field (quintessence) is given by H

10

g

i k

H

12

= 55 56 65 66 , g

i k

H

10

= 77 78 87 88 .

(3)

There is a third hermetry form whose metric is in the space S

2

× I

2

. Since this metric is a combination of an

attractive and a repulsive interaction, it is assumed that there are exist two types of particles, termed attractive and

repulsive gravitophotons. The particle for mediating this interaction is called gravitophoton because of the possible

interaction with the electromagnetic field. It is postulated from the metric of Eqs. (4) that there are two types of

gravitophotons associated with the attractive and the repulsive gravitophoton potentials. Their respective coupling

constants are denoted by

G

gp

-

and

G

gp

+

that will be described below. The attractive or negative gravitophoton

particle is described by the first term in Eq. (4), the minus sign denoting negative energy density, because it

contains the metric of the graviton, which is directly visible from Eq. (3). The repulsive gravitophoton particle is

described by the second term in Eq. (4), the plus sign denoting positive energy density, because it contains the

metric of the vacuum or quintessence particle that describes a repulsive force.

g

i k

H

11

-

= 55 56 65 66

+

57 67 58 68 ,

g

i k

H

11

+

= 77 78 87 88

75 76 85 86 .

(4)

Therefore, in Heim space H

8

there exist three physical interactions acting on material particles, namely, gravitation

represented by hermetry form H

12

(S

2

) (attractive), the quintessence or vacuum field hermetry form H

10

(I

2

)

repulsive), and the gravitophoton field, hermetry form H

11

(S

2

, I

2

) (both attractive and repulsive). Negative and

positive gravitophotons are generated simultaneously in pairs from the vacuum without extracting any energy from

---

Page 4

the vacuum. H

11

is the only hermetry form that is identically 0 that is

g

ik

H

11

=g

ik

S

2

×I

2

=0.

(5)

It seems to be strange that a hermetry form that is zero should have any physical effect at all. This reflects the fact

that the total energy being extracted from the vacuum by pair production of gravitophotons is zero. However, the

physical effect lies in the different absorption coefficients of negative and positive gravitophotons. As it turns out

in, gravitophotons are generated by virtual electrons, that is, they are generated by vacuum polarization. H

11

is the

only hermetry form that is comprised by space S

2

× I

2

, the so called transcoordinates. None of the other hermetry

forms is identical to 0, since this is the only hermetry form associated with creating pairs of particles from the

vacuum. Hence, the gravitational constant G is comprised of the three individual coupling strengths of these

interactions,

G=G

g

G

gp

-

G

q

=6.6736918 ×10

−11

(calculated value) where G

gp

-

≈1/67

2

G

g

and G

q

≈4×10

−18

G

g

.

The three gravitational forces interact with different types of matter as shown Table 2. In Eq.(6) we compare the

photon metric given by hermetry form H

5

(T

1

, S

2

, I

2

), and the gravitophoton metric, observing that the

gravitophoton metric is contained in the photon metric.

g

i k

ph

:=g

i k

H

5

=

∑

, =4

8

g

i k

and

g

i k

gp

:=g

i k

H

11

=

∑

, =5

8

g

i k

=0.

(6)

In comparison with the first term of Eq. (6), the metric for the photon can be written in the form

g

i k

ph

=g

i k

gp

g

i k

4 4

∑

, =5

8

g

i k

4

g

i k

4

.

(7)

TABLE 1. The Three Gravitational Interactions are Related to Different Types of Matter.

Generated by

Messenger particles

Force

Coupling constant

real particles

graviton

attractive

G

g

virtual particles

gravitophoton

repulsive and attractive

G

gp

+

,G

gp

-

=1/67

2

Planck mass

vacuum

quintessence or vacuum

particle

repulsive

G

q

=4.3565×10

-18

G

In Table (1) it is shown that gravitons (attractive) are exchanged between real particles, gravitophotons (attractive

and repulsive) are exchanged between virtual particles, and the quintessence or vacuum particle is due to the

vacuum itself. Therefore, for real charged particles in an accelerator the additional tensor potential does not exist.

The tensor potential only occurs if virtual particles, e.g., virtual electrons are present. This fact is important in the

experiment to measure the gravitophoton force. In the presence of virtual electrons and a suitable magnetic field,

pairs of attractive and repulsive gravitophotons can be generated from the vacuum. Only attractive gravitophotons

can interact with real particles. According to HQT, repulsive gravitophotons and gravitons can be converted into

quintessence particles. The second and third terms at the RHS of Eq. (7), can be associated with the electric force

(electric scalar potential) and the Lorentz force (vector potential). The first term represents the combined metric for

the negative and positive gravitophoton particles. If an experiment or a physical device can be conceived which

causes the metric of the photon to become 0 and make the second and third terms cancel, then the metric for the

gravitophoton particles remains. The resulting gravitational force from these pairs of gravitophotons is the basis

for the propulsion concept, termed gravitophoton field propulsion or field propulsion.

---

Page 5

In Dröscher and Hauser (2004) an experiment was suggested to measure the gravitophoton force. Above a station-

ary superconducting magnetic coil there is a rotating torus like a flywheel of some 100 kg. Due to the Heim-Lo-

rentz formula, Eq. (15), there should be a gravitophoton force generated in the rotating torus. From the Lorentz

force,

F=q E q v

T

×B ,

in our experiment v

T

denotes the velocity of the rotating torus), there follows the exis-

tence of a scalar electric potential ϕ and a vector potential A with components

A

i

=

0

Qv

i

/R

where Qv

i

denotes

the total current in the magnetic coil and i=1,2,3. However, as can be seen from Eq. (7), the metric tensor for the

photon comprises an electric potential, a vector potential, and a tensor potential, representing a new force applying

the geometrization principle of Einstein to Heim space H

8

. The complete electromagnetic interaction is therefore

given by a 4-dimensional tensor potential (ϕ, A

i

, A

ik

) with i,k =1,2,3. The tensor potential plays a crucial role in

providing the acceleration concept by converting photons into gravitophoton pairs as will be outlined in the follow-

ing section.

Acceleration Principle of Gravitophoton Field Propulsion

In the following the physical mechanism of the gravitophoton force is presented, responsible for the conversion of

photons into gravitophotons. This description is the key for devising an experiment and to providing the guidelines

for the construction of a gravitophoton propulsion device. The mechanism for the generation of the postulated

negative and positive gravitophoton particles is based on the concept of vacuum polarization, known from

Quantum Electrodynamics (QED). In QED the vacuum behaves like a dielectric absorbing and producing virtual

particles, and the Coulomb potential is associated with the transfer of a single virtual photon. Vacuum polarization

in form of the electron-photon interaction changes the Coulomb potential of a point charge for distances within the

electron Compton wavelength with respect to a nucleus. The velocities

v

i

,v

i

T

in combination with the total

charge Q in the current loop or magnetic coil need to be chosen such that

r

N

C

,

otherwise vacuum

polarization does not occur. The concept of vacuum has changed with the development of GR and it is treated now

as a a field that can have its own quantized states (Rovelli, 2003). One of its features is that it is stable and energy

cannot be extracted from it. Because of the quantum mechanical uncertainty relation new particles may

spontaneously appear out of the vacuum, termed virtual particles, e.g. Lamb shift 1947. A virtual particle may

become real (Krauss, 2000) by absorbing energy through a collision with a real particle, i.e., it does not disappear

back into the vacuum after a short period of time. Such a process is required in QFT (Quantum Field Theory) (Zee,

2003).

1. Virtual electrons: Let us consider a virtual electron produced by the nucleus of an atom in the rotating torus.

Such a virtual electron is produced according to the Heisenberg uncertainty relation.

2. Vacuum polarization: At a distance from the nucleus r

N

the virtual electron sees an electric potential generated

by the protons. A magnetic coil is used to generate a magnetic vector and tensor potential in the rotating torus

that is placed above the magnetic coil.

3. Unshielded electron charge: It is well known that for distances r

N

<

C

=

h

m

e

c

=2.43×10

−12

m

,

the Compton

wavelength of the electron, the electron charge increases because it is no longer completely shielded. The

electron potential can therefore be split into two terms, namely the shielded electron charge -e and the

additional charge -Δe.

4. Cancellation of shielded electron potential by magnetic vector potential: The terms for the electric and

magnetic potentials are of different signs as shown in Eq. (32) in Dröscher and Hauser (2004). Considering the

nucleus of one of the atoms in the material comprising the torus, there is a location r

N

for which the shielded

electric and magnetic potentials cancel, namely for

r

N

=

Z e

Q

R

c

v

i

c

v

i

T

(8)

---

Page 6

where the constant charge value Ze was used. In addition, the material in the torus should contain hydrogen

atoms to get a value of Z as small as possible, that is close to 1.

5. Linearized metric of the photon expressed by vacuum polarization constant A: With

e=Ae

where the

value of A is derived from vacuum polarization, as shown in (Landau, 1991), and a value r

N

smaller than the

Compton wavelength of the electron as well as using step 4., the linearized photon potential takes the form

h

4 4

ph

=

1

4

0

1

m

e

c

2

eQ

R

v

i

c

v

i

T

c

A−

v

k

c

v

k

T

c

.

(9)

6. Condition for vanishing photon potential: From the nature of A, it is obvious that the first term in the above

potential is generated from the vacuum, while the second term comes from the tensor potential generated in the

coil. The total energy extracted from the vacuum is, however, always zero. According to (Krauss, 2000) the

cosmological constant is 5×10

-10

J/m

3

. The third condition is, according to Eq. (9), to make the photon potential

vanish, i.e., to trigger the conversion of a photon into negative and positive gravitophotons, which requires that

A takes on a value à that is

A=

v

k

c

v

k

T

c

,

(10)

where the value of à depends on the velocities of the charges in the coil and the rotating torus. This conversion

takes place at a larger value of r, since the product on the RHS of Eq. (10) is some 10

-11

. This means that the

conversion of photons into gravitophotons begins to occur as soon as the condition

h

44

ph

≈0

is satisfied.

7. Conversion of photons into pairs of gravitophotons: A conversion of photons into gravitophotons is possible

according to Eqs. (11). The first equation describes the production of N

2

gravitophoton particles from photons.

This equation is obtained from Heim's theory in 8D space in combination with considerations from number

theory, and predicts the conversion of photons into gravitophoton particles. The second equation is taken from

(Landau, 1991)

w

ph

r −w

ph

=Nw

gp

w

ph

r −w

ph

=Aw

ph

.

(11)

8. Conversion amplitude: The physical meaning of Eqs. (11) is that an electromagnetic potential (photon)

containing probability amplitude Aw

ph

can be converted into a gravitophoton potential (pair of gravitophotons)

with associated probability amplitude Nw

gp

. From Eqs. (11) the following relation holds for gravitophoton

production, requiring the existence of a shielding potential

Nw

gp

=Aw

ph

.

(12)

The function A(r) can be calculated from Landau's (Landau, 1991) radiation correction with numerical values

for A ranging from 10

-3

to 10

-4

.

9. Three conditions for gravitophoton production: There are the following three conditions to be satisfied in order

to convert a photon into a pair of negative and positive gravitophotons, insuring that the total energy extracted

form the vacuum in form of gravitophoton particles is zero.

---

Page 7

A=

v

k

c

v

k

T

c

r

N

C

=

h

m

e

c

r

N

=

Z e

Q

R

c

v

i

c

v

i

T

(13)

The crucial point in the interpretation of Eq. (13) is that the first equation provides a value of Ã≈10

-11

. This

value is needed to start converting photons into gravitophotons. However, for this value of à the conversion

process is not efficient, i.e., the number of gravitophotons produced is too small to result in an appreciable

force. Equations two and three determine the conditions at which, according to Eq. (14) as explained below, an

effective gravitophoton potential exists for which the respective value r

N

is determined. The corresponding value

for A > Ã is some 10

-3

. It should be noted that Eq. (10) is not interpreted as a resonance phenomenon, but sets

a condition for the photon potential to disappear and the gravitophoton potential to appear that is, for the onset

of the conversion of photons into gravitophotons. Once this happened, the value of A can be increased further,

giving rise to an efficient and effective gravitophoton potential for field propulsion.

10.Metric for gravitophoton pairs generated from the vacuum: Replacing A by Eq. (12) and ensuring that the

potential of Eq. (12) identically vanishes, the converted gravitophoton field takes the form

(14)

The

∓ sign

in Eq. (14) represents the fact that there are both attractive and repulsive gravitophotons as

described by the two metric forms in Eq. (4). The sum of the two potentials adds up to 0. The gravitophoton

field is a gravitational like field, except that it can be both attractive and repulsive.

11.Different coupling constants for attractive and repulsive gravitophotons: However, the coupling constants of

the two particles are different, and only the negative (attractive) gravitophotons are absorbed by protons and

neutrons, while absorption by electrons can be neglected. This can be made plausible since the negative

(attractive) gravitophoton contains the metric of the graviton, while the positive repulsive gravitophoton

contains the metric of the quintessence particle that does only interact extremely weakly with matter. Through

the interaction of the attractive gravitophoton with matter it becomes a real particle and thus a measurable force

is generated.

12.Two-stage gravitophoton propulsion: Any gravitophoton propulsion device therefore works as a two-stage

system, first accelerating the spacecraft by the gravitophoton force and then, for certain values of the magnetic

field and torus properties, causes a transition into parallel space.

Heim-Lorentz Equations for Space Propulsion

The Heim-Lorentz equations, Eqs. (15, 16), (Dröscher and Hauser, 2004) describe the acceleration of a material

body by the gravitophoton force. Negative gravitophotons are subsequently absorbed by the protons and neutrons in

the torus which have a much larger absorption cross section compared to positive gravitophotons (Dröscher and

Hauser, 2004). The Heim-Lorentz equations that describe the gravitational interaction resulting from negative

gravitophotons are of the form (Dröscher and Hauser, 2004)

(15)

h

4 4

gp ∓

=∓

Nw

gp

w

ph

N ' w

gp

w

ph

1

4

0

1

m

e

c

2

eQ

R

v

i

c

v

i

T

c

.

F

gp

=−

p

e

0

v

T

×H ,

---

Page 8

where the index p in

p

indicates that only proton and neutron absorption processes are considered. From

(Dröscher and Hauser 2004)

p

=

32

3

Nw

gpe

w

ph

2

Nw

gpa

4

ℏ

m

p

c

2

d

d

0

3

Z .

(16)

Since the first equation in Eqs. (11) describes the conversion of photons into N

2

gravitophoton pairs, α

gp

needs to

be replaced by N

2

α

gp

. Λ

p

(dimensionless) is a highly nonlinear function of the probability amplitude of the

gravitophoton particle. The kinetic energy of the spacecraft is not provided by the magnetic field that acts as a

catalyzer in the conversion process in providing photons. In this process, no energy is extracted from the vacuum,

since gravitophoton particles are produced in pairs, attractive and repulsive.

Gravitophoton Field Propulsion Force from Acceleration

Formulas (15, 16) will be used to calculate the strength of the gravitophoton field. To increase the strength of the

interaction, a material containing hydrogen atoms should be used, because of the small value of r. A transition into

parallel space requires a magnetic induction of some 30 T and torus material different from hydrogen.

TABLE 2. The right most column shows the total gravitophoton force in Newton that would act on the rotating ring. The force

results from the absorption of attractive gravitophotons by protons.

n

N w

gpe

0

H

(T)

F

gp

(N)

10

4

2.6× 10

-14

2.0

7.14×10

-43

10

5

1.1 ×10

-5

6.3

3×10

1

10

6

1.5×10

-4

20.0

4.5×10

7

10

6

2.5×10

-4

50.0

1.45×10

9

The interaction of a gravitophoton with an electron, regardless whether real or virtual, can be neglected. The

number of turns of the magnetic coil is denoted by

n

, the magnetic induction is given in Tesla, and the current

through the coil is 100 A, except for the last row where 250 A were used. The mass of the rotating torus is 100 kg,

its thickness,

d

(diameter) 0.05 m, and its circumferential speed is 10

3

m/s. The wire cross section is 1 mm

2

. The

meaning of the probability amplitude is given in the text. For instance, if a larger spacecraft of 10

5

kg with a

rotating ring of 10

3

kg needs to have a constant acceleration of 1g, a magnetic induction

0

H

of some 13 T is

needed together with a current density of 100 A/mm

2

and a coil of 4×10

5

turns for a value

N w

gpe

=4.4×10

−5

.

The

resulting force would be 10

6

N. Thus a launch of such a spacecraft from the surface of the earth seems to be

technically feasible. The high current in the superconducting coil produces a magnetic field H. Velocity v

k

is the

speed of the charge, some 10

3

m/s, in the superconducting magnetic coil. Together with the velocity

v

k

T

of the

rotating torus, this magnetic field generates the photon conversion potential according to Eq. (9). As a future

validation activity, the magnitude of the gravitophoton force obtainable from the pulsed Sandia Z-machine (60 T)

should be calculated, and the overall experimental framework should be determined.

Space Flight using Gravitophoton Propulsion

Gravitophoton propulsion takes place in two phases. In phase one a spacecraft is subject to acceleration in ℝ

4

.

Acceleration is achieved by the absorption of negative gravitophotons through the protons and neutrons in the

torus material. Covering large interplanetary distances, would require the transition into parallel space, which is

---

Page 9

phase two of the field propulsion, involving the repulsive quintessence particle. A transition into a parallel space

leads to an increase in speed by a factor n, compared to our spacetime ℝ

4

, Eq. (18). Following the arguments by

Krauss in Millis (ed.) (1999) (a signal is needed to tell spacetime to warp, but its speed itself cannot exceed c), GR

clearly does not allow to travel faster than the speed of light in spacetime ℝ

4

. Interaction of positive gravitophotons

with spacecraft gravitons is reducing its gravitational potential, Φ, which either requires the mass of the spacecraft

to be reduced in ℝ

4

, or the gravitational constant G to become smaller. For reduced mass, conservation of

momentum would require a velocity c' > c in ℝ

4

. Due to quantum gravity theory, a quantized minimal area

=8

3 ℏG/c

3

exists. Therefore any physical phenomenon requiring a gravitational constant G' < G or a

speed of light c' > c in ℝ

4

has to be ruled out, violating the fact that τ is the minimum surface. On the other hand,

because of positive gravitophoton action, Φ is actually reduced, and thus the concept of parallel space (or parallel

universe or multiverse) is introduced, denoted as ℝ

4

(n) with n∈ℕ. For n=1, v(1):=v (velocity of the spacecraft)

and ℝ

4

(1):= ℝ

4

. It is postulated that a spacecraft, under certain conditions, stated below by Eq.(18), will be able to

transition into such a parallel space. For G(n)=G/n, M(n)=nM, and c(n)= nc, the spacecraft would transition into

n

th

-parallel space ℝ

4

(n). A parallel space ℝ

4

(n), in which covariant physical laws with respect to ℝ

4

exist, is

characterized by the scaling transformation

(17)

The fact that n must be an integer stems from the requirement in Loop Quantum Theory (LQT) for a smallest

length scale. The Lorentz transformation is invariant with regard to the transformations of Eqs. (17) that is,

physical laws are covariant under discrete (quantized) spacetime dilatations (contractions). There are two

important questions to be addressed, namely how the value n can be influenced by experimental parameters, and

how the back-transformation from ℝ

4

(n) ℝ

4

is working. The value of n is obtained from Eq. (18), relating the

field strength of the gravitophoton field, g

+

gp

, with the gravitational field strength, g

g

, produced by the spacecraft

itself,

n=

g

gp

+

g

g

G

gp

G

.

(18)

In the rotating torus, the positive and negative gravitophoton fields are generated together, and, because of energy

conservation, their strengths are equal and can be directly calculated from Eq. (15). Assuming a magnetic

induction of 30 T, a current density of 230 A/mm

2

, and 4×10

5

turns for the magnetic coil, the positive

gravitophoton field should result in an acceleration of 3×10

2

m/s

2

, in direct vicinity of the torus. Some 10 m away

from the torus the acceleration is down to some 0.1 g or 1 m/s

2

. This value for g

+

gp

is being used in calculating the

value of n for interplanetary missions. For a transition into parallel space, positive gravitophotons do interact with

the gravitons of the spacecraft, being converted into vacuum particles (sixth interaction), thus reducing the

gravitational potential of the spacecraft. Eq. (18) then determines the condition for transition into parallel space ℝ

4

(n). Since n is an integer, the effect is quantized and requires a threshold value for g

+

gp

. The result of the back-

transformation must not depend on the choice of the origin of the coordinate system in ℝ

4

. As a result of the two

mappings from ℝ

4

ℝ

4

(n) ℝ

4

, the spacecraft has moved a distance n v Δt when reentering ℝ

4

. The value Δt

denotes the time difference between leaving and reentering ℝ

4

, as measured by an observer in ℝ

4

. This mapping for

the transformation of distance, time and velocity differences cannot be the identity matrix that is, the second

transformation is not the inverse of the first one. A quantity v(n)=nv(1), obtained from a quantity of ℝ

4

, is not

transformed again when going back from ℝ

4

(n) to ℝ

4

. This is in contrast to a quantity like Δt(n) that transforms

into ΔT. The reason for this non-symmetric behavior is that Δt(n) is a quantity from ℝ

4

(n) and thus is being

transformed. The spacecraft is assumed to be leaving ℝ

4

with velocity v. Since energy needs to be conserved in ℝ

4

,

x

i

n =

1

n

2

x 1 ,i=1,2,3 ;t n =

1

n

3

t 1

v n =n v 1 ;c n =nc 1 ; G n =

1

n

G ;ℏ n =ℏ ;n∈ℕ.

---

Page 10

the kinetic energy of the spacecraft remains unchanged upon reentry. From the numbers provided, it is clear that

gravitophoton field propulsion, is far superior compared to chemical propulsion, or any other currently conceived

propulsion system. For instance, an acceleration of 1g could be sustained during a lunar mission. For such a

mission only the acceleration phase is needed. A launch from the surface of the earth is foreseen with a spacecraft

of a mass of some 1.5 ×10

5

kg. With a magnetic induction of 20 T, compare Table (2), a rotational speed of the

torus of v

T

= 10

3

m/s, and a torus mass of 2×10

3

kg, an acceleration larger than 1g is produced and thus the first

half of the distance, d

M

, to the moon is covered in some 2 hours, which follows from

t=

2d

M

/g

,

resulting in a

total flight time of 4 hours. A Mars mission, under the same assumptions as a flight to the moon, would need an

acceleration phase of 414 hours. The final velocity would be v= gt = 1.49×10

6

m/s. The total flight time to Mars

with acceleration and deceleration is 34 days. Entering parallel space, a transition is possible at a speed of some

3×10

4

m/s that will be reached after approximately 1 hour at a constant acceleration of 1g. In parallel space the

velocity increases to 0.4 c, reducing total flight time to some 2.5 hours. For an interstellar mission see (Dröscher

and Hauser, 2004).

CONCLUSIONS

In this paper a novel two stage propulsion concept, termed field propulsion, was presented that does not require

fuel and has a low energy budget. A spacecraft might attain superluminal speed by entering parallel space. The

physics of field propulsion is based on an extension of the unified field theory by B. Heim, predicting two addi-

tional, gravitational like fundamental interactions, indicated by their messenger particles, attractive or repulsive

gravitophotons and the repulsive quintessence particle. The physical mechanism for generating these particles to-

gether with an experimental set-up was discussed. It was calculated that the gravitophoton force for a magnetic in-

duction of some 20 T should be able to launch a spacecraft of 10

5

kg from the surface of the earth, resulting in a

flight time of some 4 hours for a lunar mission. Also, the conditions for a spacecraft to transition into postulated

parallel space were presented, allowing to reach higher velocities that may eventually become superluminal. As to

the credibility of HQT, it is most remarkable that most recent quantum gravity (Rovelli, 2003; Smolin, 2004) also

uses a background independent, non-perturbative formulation but currently is restricted to gravity in 4D that is, no

other forces are incorporated so far, while HQT lives in a quantized 8D space with a poly-metric, unifying all fun-

damental physics, but requiring two additional interactions, i.e., there are three quanta of gravitation.

NOMENCLATURE

à = value for the onset of conversion of photons into gravitophotons, see Eq. (10)

A = the strength of the shielding potential caused by virtual electrons

c = 2.997 924 58 ×10

8

ms

-1

, vacuum speed of light

d = diameter of the torus [m]

d

0

= diameter of the atom in its ground state [m]

-e = electron charge -1.602 × 10

-19

C

F

gp

= gravitophoton force, also termed Heim-Lorentz force, see Eq. (16)

G = G

g

+ G

gp

+ G

q

= 6.6736918 × 10

-11

m

3

kg

-1

s

-2

, gravitational constant (computed) with G

g

=graviton

constant,

G

g

≈G

that is G

g

= 6.6722037 ×10

-11

m

3

kg

-1

s

-2

(computed) describes the gravitational interaction

without the postulated gravitophoton and quintessence interactions. G

gp

gravitophoton constant,

G

gp

≈ 1/67

2

G

g

and G

q

quintessence constant,

G

q

≈4×10

−18

G

g

g

i k

gp

= metric subtensor for the gravitophoton in subspace I

2

∪S

2

g

i k

ph

= metric subtensor for the photon in subspace I

2

∪S

2

∪T

1

H = magnetic field strength [Am

-1

]

ℏ = 1.054 572 66 ×10

-34

Js, Planck's constant

m

e

= 9.109 389 7 10×10

-31

kg, electron mass

m

p

= 1.672 623 1×10

-27

kg, proton mass

Nw

gp

= Aw

ph

, see Eqs. (12, 16), i.e., gravitophoton production needs a shielding potential

N' w

gp

= w

ph

, factor introduced into Eq. (14) to demonstrate that F

gp

is a purely gravitational force

---

Page 11

n = number of turns of magnetic coil

n c = integer multiple of c, valid in parallel space, see Eq. (18)

R = distance from center of magnetic coil to location of virtual electron in torus [m]

Q = total electric charge of electrons moving in magnetic coil

r

N

= distance from nucleus to virtual electron in torus [m]

v = velocity vector of charges flowing in the magnetic coil, some 10

3

ms

-1

for superconductors

v

T

= bulk velocity vector for rigid rotating ring (torus) (see Sections. 3 and 4), some 10

3

ms

-1

in circumferential

direction, modern flywheels can reach 1,800 ms

-1

w

gp

, w

gpe

, w

gpa

,w

g_q

, w

ph_qp

, w

q

=

probability amplitudes (the square is the coupling coefficient) for,

respectively, the gravitophoton force (fifth fundamental interaction), the emission of a gravitophoton by an

electron

w

gpe

=w

gp

,

absorption of a gravitophoton by a proton or neutron, transformation of gravitophotons

and gravitons into the quintessence particle (rest mass of some 10

-33

eV, corresponding to dark energy),

transformation of photons into gravitophotons (see Eq. (11)), and quintessence particle (sixth fundamental

interaction, corresponding to dark energy)

Z = atomic number

α = coupling constant for the electromagnetic force or fine structure constant 1/137

α

gp

= coupling constant for the gravitophoton force

ε

0

= 8.854 187 817×10

-12

AsV

-1

m

-1

, vacuum permittivity

μ

0

= 4π×10

-7

Nm

-2

, vacuum permeability

τ = metron area (minimal surface, according to Heim 3Gh/8c

3

), current value is 6.15×10

-70

m

2

ACKNOWLEDGMENT

The authors are most grateful to Prof. P. Dr. Dr. A. Resch, director of IGW at Innsbruck University, for his con-

tinuous support in writing this paper. The second author was partly funded by Arbeitsgruppe Innovative Projekte

(AGIP), Ministry of Science and Education, Hanover, Germany. The authors are grateful to Roger X. Lenard, San-

dia Laboratories for providing information on Sandia's high performance magnets.

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