AIAA 2003-4990 FUTURE SPACE PROPULSION BASED ON HEIM'S FIELD THEORY

12/05/2014 22:06

aiaa2003-4990-letter.pdf (1,3 MB)

AIAA 2003-4990

FUTURE SPACE PROPULSION

BASED ON HEIM'S FIELD THEORY

Walter Dröscher1, Jochem Häuser 1,2

Institut für Grenzgebiete der Wissenschaft (IGW),

Leopold - Franzens Universität Innsbruck, Innsbruck, Austria

2Department of Transportation, University of Applied Sciences

and

Department of High Performance Computing, CLE GmbH, Salzgitter, Germany

39TH AIAA/ASME/SAE/ASEE

JOINT PROPULSION CONFERENCE & EXHIBIT, HUNTSVILLE, ALABAMA,

20-23 JULY, 2003

1 Senior scientist, 2 Senior member AIAA, member SSE, www.cle.de/HPCC, www.uibk.ac.at/c/cb/cb26/

2 The upper ring (special material) is rotating in a magnetic field possessing a radial component, giving rise to the Heim-

Lorentz force as predicted in Heim's Unified Field Theory, generated by so called gravitophoton particles.

¤¤

B I

NOW IS THE TIME TO TAKE LONGER STRIDES

-TIME FOR A GREAT NEW AMERICAN ENTERPRISETIME

FOR THIS NATION TO TAKE A CLEARLY LEADING ROLE IN SPACE ACHIEVEMENT,

WHICH IN MANY WAYS MAY HOLD THE KEY TO OUR FUTURE ON EARTH

PRESIDENT KENNEDY'S MESSAGE TO THE CONGRESS ON MAY 25, 19613

¤ 2003

Institut für Grenzgebiete der Wissenschaft,

Leopold - Franzens Universität Innsbruck,

Innsbruck, Austria

3 It does not seem that the old Europe currently has any vision of space

ABSTRACT

Effective space propulsion for interplanetary or interstellar

missions cannot be based on the momentum principle

of classical physics. This paper, being a continuation of

[1], that discussed the physical principles of Heim's unified

field theory, focuses on the properties of the predicted

gravitophoton particle (similar to the graviton) as

a means for a revolutionary propulsion system in the

sense of NASA's Breakthrough Propulsion Physics Program

(BPP) [2]. With regard to Mass, the propulsion

method does not require a propellant, since using the

gravitophoton field predicted by an extension of Heim's

field theory [1, 5-7], does allow for the conversion of

electromagnetic radiation into a gravitational like field

(i.e., gravitational interaction takes place through both

the graviton and the postulated gravitophoton particles)

that reduces the inertia of a material body. Concerning

the achievable Speed, the gravitophoton field, as a new

interaction (force) that follows from Heim's completely

geometrized unified field theory, in principle, admits superluminal

travel. The corresponding inertial transformation

(conversion of electromagnetic radiation into a gravitophoton

field) that does not exist in Einstein's four-dimensional

spacetime continuum, however, is Lorentz invariant.

Since the laws of energy and momentum conservation

[1] are strictly adhered to, the vacuum speed of

light is not the limiting velocity for an inertial transformation.

With regard to energy, there are two different

modes of propulsion. In the first mode, energy will be extracted

from the magnetic field (see Figs. 1 and 2), and

the spacecraft will be accelerated over a certain period in

time, for instance at 1g, up to a certain velocity. For a

mission to Mars the velocity would be some 1.5×106 m/s.

For an interstellar mission, a velocity of some 0.1 c is

needed. Now the second propulsion mode is employed,

reducing the inertial mass of the space craft by a factor

104. The inertial transformation will increase the speed of

the spacecraft by a factor of 104, without increasing its kinetic

energy4. Energy is needed only for the generation of

a very strong magnetic field. Otherwise, it would be impossible

to fly at speeds comparable or larger than the

vacuum speed of light. The cost of the necessary energy

to fly, for instance, a 100 ton spacecraft close to the speed

of light would be prohibitive [19, 20].

The paper comprises five sections. The first section gives

a qualitative discussion of the role of the gravitophoton

field and its double effect on matter, namely acceleration

and reduction of inertia of a material body. Section 2 contains

material about the role of the two novel particles,

the gravitophoton and probability particles. In Section 3 a

derivation of the metric tensor for moving electrical

charges in 8-dimensional Heim space, ℝ8 , is given. In the

4 Kinetic energy is calculated using the speed of light c,

c', respectively.

next section, an experiment is presented to measuring the

double nature of the gravitophoton field, and the strength

of the interaction is calculated. The most important result

is that an equation was found, termed the Heim-Lorentz

equation, that has a form similar to the electromagnetic

Lorentz force, except, that it is a gravitational like force,

while the Lorentz force acts upon moving charged particles

only. In other words, there seems to exist a direct

coupling between matter and electromagnetism. Section 5

shows the performance of the gravitophoton field as a

propulsion device. The performance of a gravitophoton

propulsion device is calculated, and a discussion is presented

of the interaction of a spacecraft traveling in some

type of hyperspace where the speed of light is greater

than the vacuum speed of light. In addition, the two-stage

nature of a gravitophoton propulsion system is elucidated

(two stage device: first acceleration, then inertia reduction).

Moreover, the performance of gravitophoton propulsion

for an interplanetary (Mars) mission and interstellar

(flight to an earthlike planet some 100 light years

away) is discussed. In the summary, the paper is concluded

with an assessment of the physical credibility of

Heim's theory and an outlook on the actual construction

of a gravitophoton propulsion device.

It should be emphasized that the introduction of new

physics, i.e., the complete geometrization of existing

physical forces, will require that some concepts of today's

physics need to be changed. It could be that in some circumstances

the introduction of the transcoordinates, Section

3.1, may invalidate the second law of thermodynamics.

It should be clear, however, if the new physics allows

for breakthrough propulsion, substantial changes to currently

established physical principles are mandatory.

Nomenclature and physical constants

Compton wave length of the electron

ℏ

=2.43×10−12

m .

c speed of light in vacuum 299,742,458 m/s ,

(1/c2 = ε0 μ0).

D diameter of the primeval universe, some 10125 m, that

contains our optical universe.

DO diameter of our optical universe, some 1026 m.

d diameter of the rotating torus, see caption Table .

dT vertical distance between magnetic coil and rotating

torus (see Fig. 2).

e electron charge -1.602 × 10-19 C.

e¤

z unit vector in z-direction.

3 of 26

Fe electrostatic force between 2 electrons.

Fg gravitational force between 2 electrons.

Fgp gravitophoton force, also termed Heim-Lorentz

force, F

gp=¤

e ¤0

vT× H , see Eq. (31).

G gravitational constant 6.67259 × 10-11 m3 kg-1 s-2.

Ggp gravitophoton constant, G

gp≈¤1 /67¤2

g i k

¤ gp¤ metric subtensor for the gravitophoton in subspace

I2∪S2 (see glossary for subspace description).

gi k

¤ ph¤ metric subtensor for the photon in subspace

I2∪S2∪T1 (see glossary for subspace description) .

h Planck constant 6.626076 × 10-34 J¤s, ℏ=h /2¤

hik metric components for an almost flat spacetime.

me electron mass 9.109390 × 10-31 kg.

mM Maximon mass, mM=

=6.5×10−8kg , without

the factor 4

2 the Planck mass is obtained.

m0 mass of proton or neutron 1.672623 × 10-27 kg and

1.674929 × 10-27 kg.

Nn number of protons or neutrons in the universe.

re classical electron radius

4 ¤¤0

2=3 × 10

−15

rge ratio of gravitational and electrostatic forces between

two electrons.

v velocity vector of charges flowing in the magnetic coil

(see Secs. 3 and 4), some 103 m/s in circumferential direction.

vT bulk velocity vector for rigid rotating ring (torus) (see

Sections. 3 and 4), some 103 m/s in circumferential direction.

wgp probability amplitude (the square is the coupling coefficient)

for the gravitophoton force

2 =G

ℏc

=3.87×10

−49 Probability amplitudes (or

coupling amplitudes) can be distance dependent (indicated

by a prime in [7]).

wgq probability amplitude for the transformation of gravitophotons

and gravitons into a particle corresponding to

dark energy (rest mass of some 10-33 eV).

wph probability amplitude (the square is the coupling

coefficient for the electromagnetic force, that is the fine

structure constant α)

2 =

4 ¤¤0

ℏc

137

Z atomic number (number of protons in a nucleus and

number of electrons in an atom)

Z0 impedance of free space,

¤0

≈376.7¤

α coupling constant for the electromagnetic force or

fine structure constant 1/137.

αgp coupling constant for the gravitophoton force .

γ ratio of probabilities for the electromagnetic and the

gravitophoton force

¤=¤w

gp¤2

=1.87×10

μ0 permeability of vacuum 4π × 10-7 N/m2 .

τ Metron area (minimal surface 3Gh/8c3), current

value is 6.15×10-70 m2.

ω rotation vector (see Figs. 1 and 2).

ω propagation speed of gravitational waves, according

to Heim ω =4/3 c.

Abbreviations

GRT General Theory of Relativity

rhs right hand side

lhs left hand side

ly light year

ls light second

QED Quantum Electro-Dynamics

SRT Special Theory of Relativity

VSL Varying Speed of Light

Subscripts

e electron

gp gravitophoton

gq from gravitons and gravitophotons into quintessence

ph denoting the photon or electrodynamics

M Maximon

R to indicate the mass of the rotating ring (torus)

sp space

4 of 26

Superscripts

em electromagnetic

gp gravitophoton

ph photon

T indicates the rotating ring (torus) of mass mR

Note: Since the discussion in this paper is on engineering

problems, SI units (Volt, Ampere, Tesla or Weber/m2

) are used. 1 T = 1 Wb/m2= 104 G = 104 Oe, where Gauss

(applied to B, the magnetic induction vector) and Oersted

(applied to H, magnetic field strength or magnetic intensity

vector) are identical. Gauss and Oersted are used in

the Gaussian system of units. In the MKS system, B is

measured in Tesla, and H is measured in A/m (1A/m =

4π × 10-3 G). Exact values of the physical constants are

given in [25].

Note: For a conversion from CGS to SI units, the electric

charge and magnetic field are replaced as follows:

e¤e/ 4 ¤¤0

and H¤ 4 ¤¤0

1 Introduction to Space Propulsion using

the Gravitophoton Field

For effective interplanetary and interstellar travel

a revolution in space propulsion technology is

needed. Such breakthrough propulsion techniques

can only emerge from novel physics, i.e.,

physical theories that deliver a unification of

physics that are consistent and founded an basic,

generally accepted principles. The theory by the

late B. Heim, developed in the fifties and sixties,

and partly published in the following three decades

of the last century, seems to be compliant

with these requirements. It also makes a series of

predictions with regard to cosmology and high

energy physics that eventually can be checked by

experiment. Most important, however, Heim's

theory5 predicts two additional interactions

(forces) [1, 5-7]. These new interactions allow

the transformation of electromagnetic radiation

into a gravitational like field, the so called gravitophoton

field. This gravitophoton field can be

used to both accelerate a material body and to

reduce its inertial mass. These effects can serve

as the basis for advanced space propulsion tech-

5 To be more precise, Heim's theory was extended to 8-

dimensions by the first author, [7], to obtain the unification

of the four known interactions (forces). In this

process, it was found that two additional interactions

occur, termed the gravitophoton field and the probability

field [1, 7].

nology, and are dealt with quantitatively in this

paper.

2 Cosmological Consequences from

Heim's Theory

2.1 Origin of the Universe

In this section we will address several fundamental

questions concerning the origin of the universe

and the creation of matter. Since Heim's

theory answers these questions in a totally different

way as does currently accepted big bang theory,

it is of great importance to find out how to

experimentally test those predictions. Heim's

theory also gives an interpretation of the physical

nature of both mass and inertia (crucial to any

advanced space propulsion system) that should

be experimentally verifiable. His theory provides

a model for a general ab initio quantized (spacetime)

cosmogony and determines the age of the

universe as well as its size and future dynamic

evolution.

2.1.1 A Quantized Cosmogony

Today, the hot big bang model of the universe

has broad acceptance [9]. According to this theory,

the universe originated from an infinitely

dense and infinitely small space. In order to describe

the very early history of the universe, i.e.,

its first 10-30 seconds, the inflationary model has

been developed by Guth (e.g., [8]), causing an

expansion of the diameter of the universe by an

extraordinary factor of some 1050 during this era.

This picture, however, is not consistent with the

physical laws that govern the expanded universe.

Moreover, the assumption of infinities or arbitrarily

large numbers seems to lack the proper

physical basis and is physically inconsistent with

the quantum principle. This principle needs to be

employed whenever wave packets cannot be isolated.

Moreover, according to [4], the probability

that the universe had an initial singularity leading

to its current shape is 1 over 10

10123

, meaning the

universe should not have developed from the big

bang singularity. In other words, in order to understand

the beginning of the physical universe,

nonphysical assumptions have to be made and

5 of 26

physical events have to be conceived that are in

stark contradiction of established physical principles.

According to Heim, such a hot big bang did not

took place. Instead, a quantized bang did take

place. The quantization principle, that is Nature

counts, i.e., only integers and not floating point

numbers are used, was present from the very beginning.

Thus any kind of singularity was impossible.

In particular, spacetime, as a physical entity,

was quantized from the very beginning. The

quantization principle, being at the very foundation

of physics, is used by Heim in a rigorous

way to obtain a unified geometrized field theory.

At the foundation of Heim's theory is the derivation

of an elemental, discrete surface quantum,

τ , denoted as Metron. The value of the Metron

size is given by ¤=Gh/2¤c2 . It should be

noted that in Heim's theory, gravitational waves

propagate at a speed of ω=4/3 c , where c denotes

the vacuum speed of light [18].

Therefore, any surface, A∈ ℝ2, cannot be a

point-continuum, but comprises a finite number,

n ∈ ℕ, of these Metrons. The current surface

area of a Metron is 6.15×10-70 m2 . The current

granularity of spacetime is extremely fine and

therefore has eluded experimental detection.

The most radical concept in Einstein's General

Theory of Relativity (GRT) is the removal of the

idea of gravity as a force. Instead, it is considered

to be a feature of spacetime curvature.

Heim extends this idea to all physical forces and

also employs the equations of GRT, i.e., their

structure, to the microcosm by quantizing these

equations in a higher-dimensional space. This approach

leads to a set of eigenvalue equations,

whose eigenvalues are the mass spectrum of all

existing material particles. As was outlined in6

[1], the phenomenon of mass thus is a purely

geometrical feature. In this context, space and

time are not the container for things, but are, due

to their dynamic (cyclic) nature, the things them-

6 In order to understand the present paper, reference

[1], AIAA-2002-2094, needs to be studied. An updated

version can be freely downloaded, see References.

selves. For a quantized unification of gravitation

and electromagnetism a 6 dimensional space is

needed. If all known interactions are to be incorporated,

space becomes 8-dimensional, ℝ8. It

was described in [1] that the metric tensor for

the 8-space can be written as a composition of

subtensors that are functions of the coordinates

from these subspaces. There are, however, selection

rules for the combination of subspaces as

described in [1]. For instance, constructing a

metric tensor from the three real coordinates of

physical space only, would not result in a metric

tensor associated with a physical interaction. Any

metric tensor that can be associated with a physical

interaction is termed Hermetry form by

Heim. Heim extends Einstein's idea, namely that

the geometry (metric tensor) of four-dimensional

spacetime causes gravity, to the 8-space. Associated

with each of these metric subtensors is a

specific physical interaction, and thus a correspondence

principle between the metric and the

actual physical interaction is established. This set

of metric subtensors, responsible for all known

as well as two new physical interactions, is denoted

as poly-metric by Heim [1, 3, 5].

However, before matter (i.e., form and inertia)

could come into existence (being represented by

the proper metric subtensor), the corresponding

length scale of the quantized spacetime of the

universe had to reach a certain threshold (minimal)

length. In other words, the metric scale had

to be fine enough to allow for the proper curvature

in physical space ℝ3. Since the universe

starts out from a quantized space, when a single

Metron covers the surface of the whole universe,

there are no problems with the initial conditions

in this picture. Evidently the Metron size is time

dependent and has decreased since the quantized

bang.

For most of the time of its existence this primeval

universe 7 possessed only structure, until its

associated elementary length scale satisfied a certain

condition. While the universe was expanding,

its associated length scale was decreasing.

When this length scale came close to the Planck

7 From now on the word universe will be reserved to

our optical universe, which is embedded in this primeval

universe.

6 of 26

length, a phase transition occurred, triggered by

fluctuations in the length scale. This phase transition

led to the generation of a particle having the

mass of the Planck mass. Heim's formula for the

mass spectrum for elementary particles (which

contains all particles, i.e. including those with

zero rest mass as well as ponderable particles)

has the form

m¤n¤=¤

¤2n¤1 /4

¤2n−1¤1 /2

¤q

with n∈ℕ (1)

and ¤= ¤c h/G¤ . Since we are interested in

the upper bound of the possible energy quanta,

i.e., in the maximum mass a particle can carry,

we choose n=1 and let ¤q=1. The exact mass formula

is given in [3, 5 see Section 3]. Therefore,

we obtain for the mass of the heaviest (neutral)

particle, denoted as Maximon (it is interesting to

note that its Schwarzschild radius is equal to the

range of its attractive gravitational field)

mM=

2¤=

c h

=6.5×10−8 kg

(2)

It should be noted that in the literature the

Planck mass is defined using ℏ and without the

factor 4

2 .

This kind of phase transition occurred at many

locations in the primeval universe, in a statistically

(random) distributed manner, and led to the

creation of many universes, separated from each

other, i.e., no optical signal can reach our universe

from such a parallel universe. These universes

should be similar with regard to their

physical laws, since they are all created by the

decay of Maximon particles. At a time of about

10100 s, when the time dependent Metron size,

¤(t), became sufficiently small, a break of a

global symmetry group must have occurred.

Each of these Maximon particles was the center

of a process for the generation of a universe, in

which ponderable particles are existing. In other

words, our own universe is the result of the decay

of one of these Maximons. This is in contrast

to the original or primeval universe that only

holds geometrical structure. The Maximon particle

decayed, cascading into mesons and baryons

(this process might be interpreted as inflationary

universe), with final products as neutrons, protons,

and electrons. This avalanche process was

accompanied by the emission of gamma quanta

that might perhaps explain the existence of the

cosmic background radiation. In addition, particles

that could be interpreted as vacuum energy

might have been created (these particles could be

interpreted as dark energy because of their very

small rest mass). Their masses corresponds to

the greatest possible wavelength possible, namely

the diameter of our optical universe, i.e., DO≈4 ×

1026 m.

It should be stressed that Heim's cosmogony

comprises a primeval universe that originated

from a quantized bang. Our optical universe,

that is of much smaller diameter, is embedded in

this primeval universe. This optical universe is

one of many other universes, created simultaneously

throughout the primeval universe, caused

by the phase transition mentioned above. This

phase transition triggered the production of the

heaviest elementary particle, the Maximon,

whose subsequent decay eventually lead to our

universe. This rapid decay, however, must have

taken place by some kind of inflationary process

or through a varying speed of light (VSL), which

is allowed in Heim's theory, if connected to an

inertial transformation.

It is important to note that during this phase

transition, mass was not conserved. Heim's universe

is a purely geometrical universe, and thus

there is a fundamental conservation law based on

length scale considerations. All other physical

conservation laws are a consequence of this fundamental

principle, see [5, Chap. 4]. The contents

of this conservation law can be stated as

4 (3)

where m0 is the mass of the proton or the neutron,

i.e., these particles are the final products,

and Nn¤ℕ is the number of protons or neutrons

in the universe.

7 of 26

It should be noted that mass is a feature of geometry,

i.e., mass is connected with a length

scale through the general equation m=ℏc / l ,

where l is a length and m denotes a mass.

In other words, since mass is inversely proportional

to a length (for instance, Compton wave

length), a decrease of the length scale leads to an

increase in mass. In that sense, the conservation

of mass is not satisfied, since it is caused by and

also depends on the geometry of the spacetime.

The generation of a Maximon particle acts as

catalyzer that triggers geometrical change in

neighboring spatial cells (denoted as Planck),

bounded by metronic (Metron) surfaces. Corresponding

to these geometrical changes is the appearance

of material particles. Knowing the end

products of the decay chain, we can compute the

number of neutrons, that are finally produced

(see Eq. (3)). We thus obtain the total mass of

our universe, which is embedded in the primeval

universe of much greater diameter of some 10125

m. This primeval universe is without mass, but

contains a large number of universes that all have

their origin in the decay of a Maximon particle.

The calculation leads to a mass of 3.71×1051 kg

of the ponderable (possessing a nonzero rest

mass) ordinary, visible matter in our universe.

With the generation of the neutron, the corresponding

interactions that result from the metric

subtensors of space ℝ8, give rise to two additional,

heretofore unknown particles, namely

gravitophotons, gph, (rest mass zero) and a very

light (unnamed) particle as well as two new

physical interactions that are the basis for the

novel space propulsion.

2.2 Cosmic Numbers

An interesting fact is that there is a relation between

the diameter of the primeval universe, D,

and the Metron size, τ. In addition, all other

physical constants can be expressed by D. In

other words, all cosmic numbers exclusively depend

upon the current diameter of the primeval

universe.

The following relations hold:

¤~D

−6/11

ℏ~D

−8/11

and G~D

−13/11

¤0~D

13/11

and ¤0~D

−3/11

(4)

Eqs. (4) show that all relevant empirical physical

quantities can be derived from the macroscopic

structure ℝ3 of the primeval universe. However,

the primeval universe has existed for an extremely

long time, so that in our own universe all

physical constants are practically invariant, since

D, at present (this presence includes the last 15

billion years), is almost constant. Eqs. (4) are a

direct consequence of the metrization of the

Heim space ℝ8.

The ratio, rge , of the gravitational and electrostatic

forces between two electrons separated at

a distance r is given by

r g e

=∣Fg

/Fe∣=4¤¤0G¤me

e ¤2

(5)

with the mass and charge of the electron given

by (see p. 33 [6])

and e=−b

(6)

where a and b are real numbers depending on π,

and Z

¤0

≈376.7¤ denotes the impedance of

free space. Inserting Eq. (6) into (5) delivers the

surprising result that also the ratio of the two

forces only depends on the size of the Metron

g e

¤ 3

3¤

¤2/ 3 (7)

Since, according to Heim, matter was generated

quite recently, compared to the cosmic time

scale, τ remained practically unchanged during

the last 15 billion years. Therefore, the intensity

of the intra-stellar thermonuclear processes must

have remained unchanged in our universe, and

thus the abundances of 3He and 4He cannot be at-

8 of 26

tributed to the change of the ratio of gravitational

and electromagnetic forces.

Cold dark matter provides for some 25% of the

mass of the universe, but is invisible. According

to supersymmetric theories, dark matter particles

have a mass of about 1011 eV, heavier than any

known particles. The name of this stable particle

is neutralino, and it would be a leftover from the

hot big bang. The existence of dark matter is inferred

from galaxy dynamics [13] that must be

present in the vicinity of each galaxy in order to

explain the observed fact that the angular frequency

of orbiting stars remains constant. Star

systems that are circling the center of a galaxy

are moving too fast with respect to the visible

mass of the galaxy. The standard explanation is

that there exists dark matter that compensates

for the missing mass. However, so far no sign of

the necessary amount of dark matter has ever

been observed, neither directly nor indirectly.

As mentioned before, in Heim's theory gravitational

waves propagate at a speed of ω=4/3 c

, which causes a major difference in the explanation

of the redshift.

Since the attractive range of gravitation is finite

(the gravitational limit depends on the composi-

8 There is doubt about this relation. ω = c could also be

possible.

9 of 26

Figure 1: The picture shows the physical principle for generating a gravitophoton field. A ring or a torus

(flywheel) of a given mass is rapidly rotating in a magnetic field created by a current loop as depicted.

The charges in the current loop (lower part), which is below the rotating mass, are moving in the opposite

direction, generating a magnetic field H (or magnetic induction B=μ0H, in practice the velocity of the

charges in the current loop are of importance), as indicated in the upper right. Using cylindrical coordinates

r, θ, and z, there should be a gravitophoton force in the negative z-direction (downward), according

to Eq. (31). This force component is the result of the circumferential velocity of the rotating ring and the

radial component of the H field. There also exists a gravitophoton force component in radial direction, r,

that is, however, balanced by the forces within the material of the rotating mass, and therefore is of no interest

to propulsion purposes.

¤¤

B I

tion of the atomic mass), a photon outside this

gravitational limit, on its way toward a distant

galaxy, would be going against a repulsive force,

caused by the total mass ahead of it, and thus experiences

an increase of its wavelength. Thus

most of the observed redshift must be attributed

to this phenomenon, and is not caused by the

Doppler effect.

3 Force Equations for Gravitophoton

Fields from poly-metric Tensor in discrete

8-Dimensional Heim Space

3.1 8D Heim Space and Subspaces

In the following, a brief roadmap for the derivation

of the force equations for the gravitophoton

field is presented. Before the gravitophoton field

can exert any force on a material body, it needs

to be generated. This is achieved by creating a

strong stationary magnetic field by a current, for

instance, in a superconducting coil, above which

a material ring (torus, flywheel) is rotated at a

high circumferential speed of some 103 m/s.

The derivation for the gravitophoton force proceeds

in three stages. First, the metric tensor for

moving electric charges is derived using modified

Einsteinian field equations, demonstrating that

from this tensor the electromagnetic Lorentz

force can be deduced. Second, the gravitophoton

potential generated in the rotating torus is presented,

and third, the physical model for the

generation gravitophoton field and its interaction

are shown. These equations are the physical

guidelines for the experimental setup, as depicted

in Fig. 1. In Section 4, the experiment to measure

the effect of the gravitophoton field on the

mass of the rotating torus is outlined in detail.

We showed in [1] that the metric tensor in 8-

space comprises several subtensors, such that

each subtensor is responsible for a different

physical interaction. In the same way the metric

tensor of Einstein's GRT acts as a tensor potential

for gravitation, the additional subtensors constructed

from the quantized Heim space, ℝ8, are

responsible for all physical interactions in our

universe. In other words, the subspaces in ℝ8 , in

which the individual metric tensors are specified,

are the cause of physical forces. In that respect,

we can speak of a completely geometrized theory.

In Heim space ℝ8 four groups of coordinates

are discerned:

1. ℝ 3 , spatial coordinates (real) (¤1, ¤2, ¤3),

2. T1, time coordinate (imaginary) (¤4),

3. S2, entelechial and aeonic coordinates

(imaginary) (¤5,¤6),

4. I2, information coordinates (imaginary)

(¤7, ¤8).

In [1] the rules of combining the various coordinates

to form the respective metric subtensors

were described. Coordinates ¤5,..,¤8 are termed

trans-coordinates. There are, however, no extra

space dimensions. All trans-coordinates are

imaginary. Any metric subtensor, in order to describe

a physical interaction, must contain coordinates

from subspaces S2 or I2.

Although a space ℝ8 is considered, all measurable

events take place in spacetime ℝ4. We consider

therefore three types of coordinates,

namely Euclidean coordinates x, and non-Euclidean

(curvilinear) coordinates η in physical spacetime

ℝ4 , while ¤ denote coordinates in Heim

space ℝ8.

The physical nature of the ¤ coordinates is such

that their mapping into our spacetime gives rise

to all known physical fields in ℝ4. The non-

Euclidean structure of these coordinates is the

underlying cause of all observed physical fields.

The following coordinate transformation, Eq.

(8), therefore represents the physical fact that

Heim space ℝ8 directly influences the events in

four-dimensional spacetime. In Heim's terminology,

all known physical fields are represented by

their respective hermetry forms (metric tensor in

admissible subspaces) (see glossary). Since, according

to Heim, the structure of Einstein's

equations, supplemented by a quantization condition,

is the fundamental set of equations governing

physical interactions in ℝ8 , the various metric

subtensors can be used to determine these physi-

10 of 26

cal interactions. The gravitophoton field (hermetry

form H11, see [1] and glossary), under the action

of conversion operator S1 (glossary), is

transformed into the so called probability field,

described by hermetry form H10 [1]. This can

formally be written as S1 H11= H10 . The physical

interpretation of this conversion could be as

follows: one dark energy particle (quintessence)

is produced from one gravitophoton and one

graviton. This means that gravitophotons and

gravitons using the transformation field wgq, are

transformed into so called dark energy particles,

q, that has a mass of some 10-33 eV, which is in

good agreement with recent findings from [13].

3.2 The metric Tensor in 8D Heim Space

In GRT a coordinate transformation between

Euclidean and curvilinear coordinates in continuous

spacetime ℝ4 is considered. In Heim's theory

a similar transformation is used, accounting,

however, for the influence of the 8D space on

events in our spacetime ℝ4. Therefore, a third set

of coordinates, ¤, is involved in the transformation.

Making use of the general coordinate transformation

xm ¤¤¤¤¤i¤¤ , one obtains for the metric

tensor

gi k=

∂ xm

∂ ¤¤

∂¤¤

∂ ¤i

∂ xm

∂ ¤¤

∂¤¤

∂ ¤k

(8)

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. The

quantum aspect of the theory is only needed for

the derivation of the spectrum of elementary particles.

For the purpose of this paper, a continuous

transformation can be used.

This metric tensor can be represented, defining

so called fundamental kernels, Eq. (9). The various

subtensors are characterized by their fundamental

kernels, ¤

i m

¤ ¤¤

. It can be shown that the

respective Christoffel symbols (termed condensors

by Heim), derived from their metric subtensors,

have tensor character, except for gravitation.

According to Heim there are so called sieve

(conversion) operators that can be applied to a

hermetry form with the effect that one or more

of the fundamental kernels become Euclidean,

i.e., the resulting metric now describes a different

physical field, marked by the new hermetry form.

For instance, this is the case for the electromagnetic

interaction, Eq. (12), that contains the metric

for the gravitophoton interaction. If the part

termed gi k

¤ em¤

, could, by some experimental

means, be made Euclidean, the gravitophoton

force would occur.

In other words, in Heim's theory operators exist

that convert one hermetry form into another one.

Our main interest in this paper is the interaction

between electrodynamics and the gravitational

like field, the gravitophoton field that can be

used to both accelerate a material body as well as

to reduce its inertial mass. Such an acceleration

does not exist in GRT, neither is a Lorentz transformation

based on a reduced inertial mass conceivable

in the framework of GRT. Thus, within

GRT, there is no way for a material body flying

at superluminal speed.

Contrary to GRT, in Heim's theory the existence

of the gravitophoton interaction, reducing the inertia

of a material body, does allow for superluminal

speeds without violating GRT.

3.3 The Metric Tensor Describing Photons

Next, the metric tensor is separated into several

subtensors. Using fundamental kernels, the metric

tensor can be written in the form

gi k

= Σ

¤,¤=1

i m

¤ ¤¤

m k

¤ ¤¤

=: Σ

¤,¤=1

gi k

¤ ¤ ¤¤

, (9)

where we defined the gi k

¤¤¤¤ different from [1],

this being a matter of convenience only. As we

showed in [1, Eq. 12], the hermetry form

5=H

5 ¤ I

1¤ 9 is responsible for photons

and depends on the subspaces I2, S2, and T1 with

9 Contrary to [1], subspaces are denoted by superscripts

instead of subscripts.

11 of 26

coordinates ¤4, ¤5,...,¤8. The respective metric

tensor for photons is

gi k

¤ ph¤

= Σ

¤ ,¤=4

gi k

¤ ¤ ¤¤ (10)

where the superscript ph 10, denotes the metric

subtensor for the photon. The new gravitophoton

field that originates from the poly-metric of

Heim's extended theory [1, 7] is described by

hermetry form H11, H

11=H

11¤ I

2¤ depending

on the subspaces I2 and S2 with coordinates ¤5,...,

¤8. Its metric tensor is given by

gi k

¤ gp¤

= Σ

¤,¤=5

gi k

¤ ¤ ¤¤ (11)

where the superscript gp denotes the metric subtensor

for the gravitophoton. Comparison of

Eqs. (10) and (11) leads to

gi k

¤ ph¤

=gi k

¤ gp¤

¤gi k

¤ em¤ (12)

where gi k

¤em¤ is defined by

gi k

¤ em¤

:= Σ

¤,¤=5

gi k

¤ ¤ 4 ¤

¤gi k

¤ 4 ¤¤

¤gi k

¤4 4¤ (13)

and is part of the electromagnetic interaction and

thus the index em was used. However, it should

be noted that this part of the metric tensor has no

physical meaning. It is only the metric tensors of

Eqs. (11 and 12) that correspond to physical interactions.

This interpretation becomes clear,

since Eq. (12) shows that hermetry form H5, denoted

as the photon field, actually contains the

metric of the gravitophoton field. We interpret

this part of the metric in Eq. (10) as coupling potential

between the electromagnetic and the

gravitophoton field. It is exactly the metric of the

gravitophoton particle. However, there is no

gravitophoton interaction coming from Eq. (12).

10 We adopt the convention of using an abbreviation as

a superscript to denote the physical meaning of various

metric subtensors, instead of using symbols like '

, '' or ~ etc., for the sake of clarity.

Only by employing the proper sieve (conversion)

operator, the metric of Eq. (12) can be converted

into the metric of the gravitophoton field. Only

then, a gravitophoton field would occur. In that

respect, separating the metric for the photon, Eq.

(12), into two terms is somewhat misleading. It

does not mean that the electromagnetic field

comprises a gravitophoton field and a second

part. It does show, however, that conversion between

the fields is mathematically possible. According

to Heim's extended theory (from 6 to 8

dimensions, see [7]) there exists a transition operator

S2 (not to be confused with subspace S2)

that causes this photon-gravitophoton interaction,

that is, a transformation of a photon into a

gravitophoton, and is symbolically written as S2

H5 = H11.

Since only metric tensors (geometry) were considered

so far, no guidelines are available how

this conversion can be realized by experiment.

How this purely mathematical transformation can

be brought into concrete physical existence is a

most important question, and is addressed in sections

3.4 to 3.7.

3.4 The Metric Tensor for Moving Charged

Particles

Making use of the coordinate transformation

xm¤¤¤¤¤i¤¤ one obtains from Eq. (10) the representation

for gi k

¤ ¤¤¤ in the following form

gi k

¤ ¤¤¤=

∂ xm

∂ ¤¤ ¤¤

∂¤¤ ¤¤

∂ ¤i

∂ xm

∂¤¤ ¤¤

∂ ¤k

(14)

For weak gravitational fields, spacetime is almost

flat, so the contribution of

∂¤4

is large in comparison

∂¤4

∂¤l

, l=1, 2,3 . Introducing the abbreviations

12 of 26

hm4 :=Σ

¤=5

gm4

¤ ¤ 4 ¤

h4 l :=Σ

¤=5

g4 l

¤ 4 ¤¤

h4 4 :=g4 4

¤4 4¤

hm l := Σ

¤,¤=5

gm l

¤ ¤ ¤¤

(15)

where m=1,...,4 and l=1,2,3.

Now the first stage of the derivation can be performed.

It is investigated whether there exist

modified Einsteinian field equations that provide

a metric for describing the motion of electric

charges. The important difference to Einstein's

GRT is that a transformation

ℝ4 ¤ ℝ8 ¤ ℝ4 takes place, resulting in a metric

tensor not available in GRT. Einstein's field

equations are therefore used as structural equations

only in a discrete 8D Heim space. In this

space a metric exists that is rich enough to account

for the four fundamental forces and their

mediator particles, but, as was stated before,

gives rise to two additional interactions.

Ri k=¤¤T i k−

gi kT ¤ (16)

And T=T k

k . In the gravitational case, κ is of

the form ¤=

8¤G

c4 , while for our considerations

κ needs to be adjusted to the electromagnetic

hermetry form.

For weak electrodynamic and also for weak

gravitational fields, spacetime must be almost

flat, so one obtains

gi k=gi k

¤ 0¤¤hi k where g00

¤ 0¤=−1 and

gi i

¤ 0¤

=¤1 , and all other components are 0. The

hi k are small quantities whose products are

negligible. It is well known that the linearized

Ricci tensor can be written as (see, for instance,

[17], p. 298)

Ri k=½□2 hi k (17)

where □2 = g

¤ 0 ¤ i k ∂2

∂ xi∂ xk

=∇2−

∂2

∂ t2 is the

D'Alembertian operator. Einstein's equations can

thus be written in the form

□2 hi k =

∂2 hi k

∂ xn

2 =2 ¤¤T i k−

gi k T ¤ (18)

with summation over index n. Eq. (18) is an inhomogeneous

wave equation, whose solution is

given by the so called retarded potentials.

The components of the stress-energy-momentum

tensor are of the following form [17]

T i k=¤vi vk

and T=¤c2 since vi

, vk≪c .

For a point-like mass M, the following relation

holds

∫T

i k

dV=M v

k . The partial differential

equation (18) can be solved by means of Fourier

transformation (see, for instance [17], page 217).

This eventually leads to the result

hi k=

4¤¤0

me c

c (19)

where the charge Q is a multiple of the electron

charge and i,k =1, 2, 3. It should be noted that

hik are dimensionless quantities.

It is well known from QED that the electric

charge is proportional to the coupling amplitude

(or probability amplitude), see [26] Chap 13,

e= ¤4¤¤0 ℏ c ¤¤ and thus Eq. (19) can be

written as

hi k=¤

ℏ

me c

(20)

The meaning of the above equations is that the

movement of charges causes a metric hik, as described

in Eq. (19). From Fig. 1 it can be seen

that a charge Q (here the simplification is made

describing charges in the magnetic coil by a single

charge Q) is moving with velocity components

vi in a magnetic coil (current).

13 of 26

3.5 The Metric Tensor for Gravitophotons

In the second stage, the gravitophoton metric

tensor can be directly found from Eq. (20), observing

that the metric for the moving charged

particle is proportional to the fine structure constant

α. In the same way, it is concluded that the

metric for the gravitophoton tensor components

is proportional to αgp, the coupling constant for

the gravitophoton force. Therefore, the ratio of

the metric for a moving charged particle and a

gravitophoton particle equals α /αgp.

Thus the metric for the gravitophoton particle is

given by

hi k=¤gp

ℏ

me c

(21)

where ¤ :=wph

2 =

4¤¤

ℏ c

and

gp :=wgp

2 =Ggp

ℏ c

Inserting αgp, Eq.(21) takes

the form

hi k=Ggp

(22)

The potential derived from the metric of Eq. (22)

is denoted as gravitophoton potential. The constant

for the gravitophoton field, Ggp, is analogous

to the gravitational constant G.

The following relation holds

Ggp

=¤wgp

wg¤2

G≈

672

G .

It is important to note that from the metric tensor

components hik,, Eqs. (20, 22), respective

potentials for a moving charged particle and a

gravitophoton particle can be obtained. However,

the ratio between these two potentials is

equal to the ratio of their corresponding probability

amplitudes, and not of their coupling constants

(probabilities). The reason for this is

straightforward to observe. For instance, in Eq.

(20), the product of two charges e and Q occurs.

Their product is proportional to α. The respective

electrostatic potential contains a single

charge only, and thus the factor is ¤¤¤ .

It is important to observe that the metric of

Eq.(20) corresponds to a Lorentz force, where

the first part of the metric, eQ /r vi / c , is associated

with the magnetic field and the second

part, vk

T / c with the velocity of a material body

(in our experiment this is the rotating torus).

Since the gravitophoton metric differs from the

metric of Eq. (20) only by the factor αgp / α the

force that a single gravitophoton exerts is given

gp=

¤gp

e ¤0

vT× H (23)

If the force acts on an electron, me has to be

used, for a proton the mass mp has to be inserted

into αgp. Gravitophotons can either be absorbed

by electrons or by protons.

In order to get an appreciable gravitophoton

force, a large number of gravitophotons per volume

and time unit needs to be generated, see

Figs. 1 and 2 for the experimental setup. The interesting

fact is that Eq. (23) allows both to control

the magnitude and the sign of the gravitophoton

force. The gravitational action of a gravitophoton

is similar to a graviton, except that

gravitophotons can be generated through electromagnetic

interaction and the force can reverse

sign.

The question arises under which conditions

gravitophoton fields exist that can propagate into

the surrounding space. Following Heim [7], a

brief description how to compute the probability

amplitudes for the photon conversion into gravitophotons

was presented in [1]. Similar to a dielectric,

quantum theory and relativity require

that for short times so called virtual pairs of electrons

and positrons may be present in the vacuum.

If there is an electric field present, suppose

in form of a point charge, the positive charges of

the virtual particles are displaced relative to the

14 of 26

negative ones, known as polarization of the vacuum.

For large distances, r, this leads to a shielding

of the point charge. In a macroscopic experiment

one sees this shielded charge, whereas only

for very small r, the bare, unshielded charge becomes

visible. The scale of the spatial displacement

is set by the length ℏ/mec, associated with

the mass of the electron. The time of existence

for a virtual electron-positron pair is about

ℏ/mec2, which is some 10-21 s.

3.6 The Physical Picture: From Photons to

Gravitophotons

Before the force equations for the gravitophoton

field are derived, i.e., their interaction with a material

body, it is appropriate to present a qualitative

picture of the transmutation of photons into

gravitophotons. The gravitophoton field is a

gravitational like field, except that it can be repulsive

or attractive. It can both accelerate a material

body and reduce its inertia. Any propulsion

device therefore would be a two-stage system,

first accelerating the body and then reducing the

inertial mass of the body.

The mathematical description for the conversion

process is given by the first equation in Eq. (24).

In the following, the physical mechanism is presented,

responsible for the conversion of photons

into gravitophotons.

The physical mechanism for the generation of the

postulated gravitophoton particles is based on

the concept of vacuum polarization from QED.

In QED the vacuum behaves like a dielectric absorbing

and producing virtual particles.

The high current in the possibly superconducting

coil produces a magnetic field H where vk is the

speed of the charge in the current loop or coil

(Figs. 1 or 2, respectively). Together with the

velocity vk

T of the rotating torus, this magnetic

field generates the conversion potential according

to Eq. (22). This potential interacts with the

virtual photons generated in the vicinity of each

of the atomic nuclei (field point), comprising the

material of the rotating torus.

The nuclei (positive charge) are continually emitting

and absorbing virtual photons. Some of the

photons create electron-positron pairs that subsequently

annihilate. Virtual electrons are attracted,

positrons are repelled by the positive

charge of a nucleus, resulting in vacuum polarization.

Thus the real positive charge is partially

shielded and cannot be measured, until one is inside

the shielding region. The positive charge is

higher closer to the nucleus, since the shielding

effect is reduced. The shielding distance is given

by the Compton wavelength of the electron,

which is ¤C=

ℏ

=2.43×10−12

m . Therefore the

probability amplitude, wph, which is proportional

to the electron charge, will increase at distances

smaller than λC. Virtual photons are the interaction

particles between the electric field of a nucleus

and the virtual electron. In addition, at the

location of each nucleus, the coupling potential

of Eq. (22) is effective. The higher the difference

between the unshielded and the shielded probability

amplitudes, wph, the higher the number of

virtual photons, as shown in the second equation

in Eq. (24). The number of virtual electrons is

proportional to the number of virtual photons.

Gravitophotons are emitted by the virtual electrons.

Thus the number of gravitophotons should

be proportional to the difference in the probability

amplitudes. Hence, the conversion from photons

to gravitophotons must take place close to

the nucleus within the the shielding distance λC.

In order to achieve this goal the conversion potential

must be strong enough to generate a distance

r, measured from the nucleus to the location

of the virtual electron, that is much smaller

than λC. This condition sets a strict requirement

for the parameters determining the magnitude of

the conversion potential, namely the velocities

T and vk.

The gravitophotons are subsequently absorbed

by the protons in the torus which have a large

absorption cross section compared to the electrons.

In the non-relativistic case, the scattering

cross section for photon-electron interaction is

given by ¤=

8¤

2 , see [27], where re is the clas-

15 of 26

sical electron radius, given by

4 ¤¤

2 ℏ

c . For gravitophotons wph

has to be replaced by Nwgp, since in the conversion

process from photon to gravitophoton, N

gravitophotons are generated according to

Eq. (24). It should be noted that the factor N

does not occur in Eq. (23), since it depends on

the conversion process. Thus the absorption

cross section for a gravitophoton particle by a

material particle (here the electron is used) is

given as ¤

8¤

¤Nw

gp¤4¤ ℏ

c¤2

. However, if

the absorption is by a proton, the electron mass

me is to be replaced by the proton mass mp.

Therefore the absorption cross section of a proton

is larger by the factor mp/me. Hence, the absorption

of gravitophotons by electrons can be

neglected.

In the next section, this formula 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.

3.7 Force Equation on a Material Body exerted

by Gravitophotons

In the third and final stage of our derivation, the

bulk equations of motion for a material body exerted

by gravitophoton particles need to be determined.

To this end, Eqs. (24) are used

w ph ¤ r ¤−w¤=Nwgp

w ph ¤ r ¤−w ph=Aw ph

(24)

The first equation in (24) describes the production

of N2 gravitophoton particles11 from photons

with respect to so called conversion potential wκ.

This equation is obtained from Heim's theory in

8D space, in combination with a set algorithm,

and predicts the conversion of photons into

gravitophoton particles. In particular, it is emphasized

that the metric for the photon, Eq. (12),

11 The factor N2 results from the fact that in Eq. (24)

probability amplitudes are considered, but the generation

of particles depends on actual probabilities.

already contains the metric for the gravitophoton

particle, Eq. (11)12.

The second equation in (24), obtained from

QED, see [27], describes the screening of the

charge of a nucleus by vacuum polarization

through virtual electron-positron pair production.

It should be noted that probability amplitudes

correspond to physical potentials [26]. The

coupling amplitude w

ph ¤r ¤ is the probability

amplitude depending on the distance from the

nucleus, and describes the partially shielded potential

of the nucleus [26], Chap. 13. At distances

larger than the Compton wavelength,

ph ¤r¤=

¤137¤

which is the square root of the

fine structure constant α.

Next, the potentials corresponding to the probability

amplitudes need to be identified :

1. w

ph ¤r ¤ is interpreted as the potential of the

nucleus seen by a virtual electron,

4 ¤¤0

r .

2. Since the potential in 1. is a scalar potential,

the potential representing wκ should also be a

scalar potential. From the discussion in Section

3.5 the following potential is assumed:

4¤¤

me c

(25)

This leads to the following equation between the

associated potentials

4¤¤

me c

2¤e Ze

−

c¤ =

Nwgp

wph

Ggp

(26)

12 This essential equation is stated without proof. The

theory of the coupling constants is too comprehensive

to be treated in this paper. However, since the metric

of the photon contains the metric of the gravitophoton,

this could be considered as some kind of evidence

for the possibility of such a conversion.

16 of 26

where the factor α/αgp is the ratio of the coupling

constants of the electromagnetic and the gravitophoton

force. Since the rhs of Eq. (26) is very

small, it is treated as 0. This leads to the equation

for r

r≈

Z e

T (27)

From Eq. (27) it is obvious that in order to have

a small value of r, that is r < λC, the total charge

Q, the velocity of the charges vi, and the rotation

speed of vi

T of the torus should be chosen as

large as possible. The torus should also have material

that contains hydrogen atoms.

In the next step, the unknown gravitophoton

production factor Nwgp has to be calculated.

This factor comprises two terms, namely the absorption

of the gravitophoton by an electron or

by a proton. The absorption of gravitophotons

by electrons is not taken into account, because of

the much smaller absorption cross section.

From the physical model outlined in Section 3.7,

it is concluded that the number of gravitophotons

emitted is proportional to the number of virtual

electrons, which depend direcly on the difference

of the coupling amplitudes, second equation in

(24). Therefore, it is assumed that the relation

Nwgp=Aw ph (28)

holds. Here the proton mass is used. The function

A is obtained from radiation correction ,

3¤

¤∫

∞

e−2me r ¤ ¤1¤

2¤2 ¤¤¤2−1¤1/2 /¤2

d ¤ ,

i.e., from the virtual electron-positron pair

shielding of the charge of the nucleus, for a derivation

see [27].

For the emission of a gravitophoton by a virtual

electron, the coupling constant is given by

gpe

ℏc

. For the absorption process the

coupling constant has the form w

gpa

ℏc

Using the absorption cross section for protons

from Section 3.7, the probability for this process

is obtained as

3 ¤Nwgp¤4¤ ℏ

mp c¤2

Z (29)

With Eq. (29) the total force on the rotating

torus can be determined. The first equation in

(24) describes the conversion of photons into N

gravitophotons. Therefore, αgp needs to be replaced

by N2 αgp .

=w N

2 ¤gp

e ¤0

×H (30)

Multiplying Eq. (30) by probability w from Eq.

(29) results in the total force of the gravitophotons

on the rotating body

gp=¤

e ¤0

vT×H (31)

where ¤

p indicates that only proton absorption

processes were considered. From Eqs. (29)

and (30) ¤

p is determined as

3¤Nwgpe

w ph ¤2

¤Nwgpa¤4¤ ℏ

mp c¤2

Z ¿

(32)

Λp (dimensionless) is a highly nonlinear function

of the probability amplitude of the gravitophoton

particle. d is the diameter of the torus, d0 the diameter

of the atom in its ground state, and Z denotes

the atomic number of the atom.

17 of 26

18 of 26

Figure 2: Instead of a simple current loop, a coil with many turns can be used. The field of this coil gives rise

to an inhomogeneous magnetic field that has a radial field component. The radial component and the gradient

in z-direction are related through H

=−

∂ H

∂ z

. It should be noted, however, that if the ring possesses a

magnetic moment, M, there is a magnetic force in the z-direction of magnitude F=M

∂ H

∂ z

. This force does

not depend on the rotation of the ring. For a diamagnetic material the force acts in the positive z-direction

(up), while para- and ferromagnetic materials are drawn toward the region of increasing magnetic field

strength (down). The gravitophoton force comes into play as soon as the ring starts rotating, and superimposes

these effects. Perhaps equipment used to measuring magnetic moments can be employed to determine

the gravitophoton force. For instance, if a diamagnetic substance is used, the gravitophoton force (down)

could be used to balance the magnetic force, so that the resulting force is 0. From Refs. [23 and 24] it is found

that a quartz sample (SiO2, diamagnetic) of a mass of 10-3 kg experiences a force of 1.6 × 10-4 N in a field of

Bz=1.8 T and a gradient of dBz/dz=17 T/m. A calcium sample (paramagnetic) of the same mass would be

subject to a force of -7.2 × 10-4 N. It is important that the material of the rotating ring is an insulator to avoid

eddy currents.

¤ ¤

¤¤

B I

For the experiment outlined in Section 4 it is assumed

that a material ring of a given mass of

some 100 kg (torus) is rotating in the x-y (or x1-

x2) plane. Below that ring, a current I carrying a

total charge Q is flowing through a magnetic

coil, located in the x-y plane (see Fig. 12). According

to Eq. (31) there should be an interaction

between the moving charge Q (current

through the magnetic coil) and the moving

charges (electrons) of the rotation ring.

We therefore have shown, starting from Eq.

(12), which describes the underlying metric for

the electromagnetic interaction, that this metric

can actually be used to produce the so called

Heim-Lorentz force. Hence, the correspondence

between metric and physical interaction

has been demonstrated.

4 Experiment to determining the double

Nature of the Gravitophoton field

The experiment comprises a rotating ring (torus)

of a certain mass and a super-conducting magnetic

coil, whose inner radius is small in comparison

to its outer radius. Let the magnetic coil be

located at a distance, dT, below the torus. The

circumferential speed, vT, of the torus is supposed

to be 103 m/s. The coordinate system is

chosen such that the midpoint of the magnetic

coil is at the origin. The torus rotates in the x-y

plane, with the z-axis pointing upwards. It is assumed

that the volume of the coil is sufficiently

small, so that the retardation effect for all points

within its volume may be neglected.

The gravitophoton force on the rotating torus of

mass mR is given by Eq.(32), which is surprisingly

similar to the electromagnetic Lorentz

force. It was termed the Heim-Lorentz force by

these authors. This equation describes the complete

conversion of magnetic field energy into kinetic

energy. This equation is the basis for the

gedanken-experiment depicted in Fig. 1. It

should be noted that the sign of the force depends

on the direction of the velocity of the rotating

body. As a rule, the velocity of the charges

in the current loop and the circumferential velocity

of the rotating ring must be in opposite directions,

see Fig. 1.

As numerical examples, four cases are investigated.

It turns out that the Heim-Lorentz force is

strongly nonlinear, and without proper adjustment

of current I, rotation speed, and the proper

number of turns for the magnetic coil, it cannot

normally be observed.

Three different magnetic coils are considered,

with 104, 105, and 106 turns. A wire-thickness of

1 mm (10-3 m) is chosen. The resulting magnetic

induction is 1.2 T, 6.3 T, 20 T, and 50 T.

The thickness of the torus (ring) is 0.05 m with a

mass of 100 kg.

It is known that the current density decreases exponentially

within a conductor. The skin depth,

δ, measures, for a particular material and frequency,

the depth at which the current density in

the material has decreased to 1/e, compared to

the value at the surface. The value 10-7 m was

chosen for our example calculation. Together

with an electron velocity of 103 m/s, this results

in a total charge Q of 4×105 As. With a value of

0.5 m for dR, Table shows the gravitophoton

force acting on the rotating torus. Using a magnetic

field strength of some 20 T, a force of some

44 N is obtained for a ring rotating at a speed of

103 m/s and a mass of 100 kg. At the very high

magnetic field of 50 T the total force should be

2.7 ×103 N.

19 of 26

n Nw

gp ¤0

(T)

Fgp

(N)

104 2.6× 10-14 2.0 1.4×10-58

105 1.1 ×10-5 6.3 2.8 ×10-6

106 1.5×10-4 20.0 4.4 ×101

106 2.5×10-4 50.0 2.7 ×103

Table1: The right most column shows the total gravitophoton

force in Newton that would act on the rotating ring. The force

results from both processes, namely the absorption of the gravitophoton

by an electron and a proton. The absorption through a

proton results in a much larger force, so that in principle 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 field 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) 0.05m, and its circumferential

speed is 103 m/s. The wire cross section is 1 mm2.

The meaning of the probability amplitude is given in the text.

Because of the highly nonlinear character of Λ

p with respect to

gp, the resulting force varies from actually 0 to 2.7g. It should

be mentioned that there are type II superconductors that can

sustain a magnetic field of up to 34 T13.

The experiment described is based on two well

known ingredients, namely a magnetic coil and a

rotating body of mass or flywheel. The interaction

is between the charges (electrons) flowing in

the magnetic coil and the electrons of the atoms,

rotating with the flywheel.

There is perhaps another way to measure the

gravitophoton field, namely directly on the

atomic scale. Eq. (23) describes the gravitophoton

force between a single electron and a charge

Q. Let us consider a single atom in a so called

magnetic micro trap [21]. This trap comprises

micro-electromagnets with micro-fabricated Cuwires

of a width of several μm through which a

current is flowing. Special potentials can be produced

to manipulate the atom that can move in

the axial direction. According to Eq. (31) a

gravitophoton force between the charges in the

Cu-wire and the atom should occur. However,

there is also a force acting on the magnetic moment

of the atom because of the inhomogeneous

13 The most recent analysis, too late to be included in

this paper, shows that substantially larger forces may

occur if the recoil virtual electrons are subject to due

to emission of gravitophotons is included in the momentum

budget.

magnetic field, which would superimpose the

gravitophoton field. This experiment needs to be

considered in more detail in order to find out,

whether the gravitophoton force could be detected.

Another possible source for the gravitophoton

field is on the cosmological scale. It is reported

that neutron stars that are pulsars have a magnetic

induction of some 108 T. Atoms or molecules

moving in this very strong field should be

subject to a gravitophoton force, resulting from

Eq. (31). The question of course is, how to actually

observe this effect, separated from all other

forces. A neutron star of some 10 km diameter

and a mass of about three times the sun's mass,

may rotate rapidly at hundreds of revolutions per

second [22].

5 Performance of the Gravitophoton

Field as a Propulsion Device

In the following, we will do two gedanken-experiments

for a gravitophoton propulsion device.

First, we consider an interplanetary mission to

Mars. Second, an interstellar mission to a planet

100 ly away from earth is discussed.

5.1 Interplanetary Mission

In order to use a gravitophoton device as a propulsion

system that can launch a spacecraft from

the surface of the earth into outer space, the

gravitophoton field that acts normal to the plane

of rotation should be able to lift the spacecraft,

i.e., the acceleration of the spacecraft must be

larger than 1 g (9.8 m/s2). Using these values, the

magnetic induction of 50 T should be able to

launch a spacecraft with a mass of 3× 104 kg, accounting

for losses, see Table 1. For a mission

to Mars, whose average distance from earth is

some 900 ls (light seconds), which amounts to a

distance s of 2.7×1011 m. A non relativistic calculation

leads to a flight time

=1.6×10

s for half of the distance,

and a total flight time of 3.7 days. The peak velocity

of the spacecraft would be some 1.5×106

m/s, which is, compared to chemical propulsion a

20 of 26

very high, but still non-relativistic speed. For this

interplanetary mission, only the accelerative nature

of the gravitophoton field has been used. In

order to do an interstellar mission, superluminal

speeds are necessary, which can only be achieved

by the so called inertial transformation, where

the gravitophoton field is used to reduce the inertial

mass of the spacecraft by converting electromagnetic

radiation into gravitophotons.

5.2 Interstellar Mission

The interstellar mission to a planet some 100 ly

away from earth would take place in two stages.

In stage one, lasting 30 days, the spacecraft

reaches a speed of some 0.1c, using gravitophoton

acceleration. In stage two, the inertial mass

of the spacecraft is reduced by a factor of 10-4.

To this end a magnetic field is needed that is of

the same magnitude as during the acceleration

phase. In addition, fine tuning is needed to reduce

the gravitational field of the spacecraft. Because

the ratio of the initial and the reduced inertial

masses is proportional to the ratio of the final

and initial velocities of the spacecraft (see

[1], which follows directly from the conservation

of momentum and energy), the final speed of the

spacecraft is 103 c. The spacecraft would travel

in some kind of hyperspace in which the speed of

light c' = 104 c. The total travel time would be

0.1 y + 2×30 d, which is approximately 3

months. A return trip would be feasible in 6

months time. A major advantage would be that

during 4 months, the astronauts would be subjected

to an acceleration of 1 g.

The question arises of what will happen to the

astronaut flying at a cruising speed close or

higher to the vacuum speed of light and eventually

flying back to earth. The so called twin paradox

should not play a role, since the denominator

in the Lorentz transformation does not change,

because v

' / c

'=v / c where primed quantities

denoted values in hyperspace. This relation follows

directly from momentum conservation.

Thus the question which twin aged more is not a

relevant one.

SRT introduces the vacuum speed of light, c, as

the upper speed limit. One might argue that exceeding

the vacuum speed of light during an interstellar

flight, might cause a change in the uncertainty

relation ¤ x ¤ px≥ℏ . Inserting the

value mc for the uncertainty of the momentum

leads to ¤ x≥ℏ/ mc , it is not the value of c,

but the total momentum that restricts the uncertainty

in the location. However, as was said before,

an inertial transformation leaves the momentum

of the vehicle unchanged.

Conclusions and Future Work

In the present paper an outline of some of the

features of Heim's fully geometrized, unified field

theory was given. The most important aspect is

his discrete spacetime in 8 dimensions, with a

minimal (quantized) surface element, the so

called Metron. As a physical consequence, the

universe started in a quantized bang, with well

determined initial conditions. During the expansion

of this primeval universe, the associated

length scale became smaller. When the length

scale reached the value of the so called Planck

length, matter could be created, and a phase

transition took place. According to Heim's formula

for the mass spectrum for all existing particles,

the heaviest particle, the Maximon, associated

with this length scale, was generated. This

effect took place at the same time at many locations

in the primeval universe. The Maximon rapidly

decayed, with the stable particles, namely

electrons and protons along with high energy

photons as end products. This decay process

took place as some kind of inflationary process.

Each of these Maximons was the cause of a new

universe. Matter was not conserved, instead, the

inflationary process was governed by Eq. (3)

that allows to calculate the mass of our present

universe, which is embedded in the primeval universe.

Heim's theory is an extension of Einstein's theory

in that each physical interaction and its associated

interaction particle is described in a quantized

higher dimensional space. In other words,

all forces and all material particles are of geometric

origin. Elementary particles possess a complex

dynamic structure that also exhibits zones

within such a structure. In the 8-dimensional

21 of 26

space, termed Heim space by the authors, several

metric subtensors can be formed. Each of these

subtensors, called a Hermetry form, is responsible

of a physical interaction or interaction particle

[1]. When these metric subtensors are

formed, two new additional interactions along

with their interacting particles occur. One of

these particles, termed the gravitophoton, is responsible

for the reduction of the inertial mass of

a material body (spacecraft). This physical effect

would lead to an inertial transformation in the

Lorentz matrix, that, in principle, allows for superluminal

travel, because of the conservation of

momentum and energy. The kinetic energy of the

spacecraft, flying at a velocity greater than the

vacuum speed of light, has not increased, since

its inertial mass decreased. Otherwise, any spacecraft,

flying at velocities close to c, would need

an amount of kinetic energy that is impossible to

supply and to pay for.

In that respect, the goals of NASA's Breakthrough

Physics Propulsion Program, namely,

no fuel, superluminal speed, and no excessive

amounts of energy needed for a revolutionary

space propulsion system can be met, provided, of

course, that Heim's theory represents physical reality.

Again, as was said in [1], the authors are aware

of several shortcomings in this paper. Not all of

the physical features of Heim's theory were derived

properly. Some of the conclusions are

based on a somewhat speculative physical model

concerning the generation of gravitophoton particles.

It should be mentioned that Heim's legacy is very

large, several thousand pages, and his presentation

style is not the one of contemporary physics.

Heim uses his own terminology that needs to be

translated into the language of modern physics.

In addition, since his theory is completely geometric,

there are many concepts that have no

counterpart in modern physics. Whether his theory

is actually true, can only be determined by

experiment. One of the most important predictions

is that of Section 4, exploiting the nature of

the gravitophoton field.

In conclusion, it can be said that the gain, if this

theory were true, will be close to infinity, while

the probability of success may be close to zero,

the product of these two numbers remains undetermined.

The risk, however, to investigate in the suggested

experiment seems to be relatively low. If

found to be true, a genuine revolution of space

flight could be the outcome. Such a propulsion

system might even be simpler than existing rockets,

based on highly complex chemical propulsion.

Needless to say, if the proposed reduction in inertial

mass could be confirmed by experiment,

not only a revolution in space transportation, but

also in ground transportation would take place.

Heim's theory currently is not mainstream physics,

but it contains several highly interesting

ideas, and its geometric origin of the physical

world, is appealing, at least to the authors. As far

as the authors understand Heim's theory (many

of his calculations remained unchecked so far,

simply because of the amount and the difficulty

of his work), Heim seems to have achieved a

consistent mathematical formulation that describes

all physical interactions in geometrical

terms. In that respect, he has realized Einstein's

original idea, but ascribing space, namely the 8

dimensional Heim space (3 real coordinates

comprising physical space and 5 imaginary coordinates)

many additional, unusual features.

Future work will focus on a more precise prediction

of the gravitophoton field with emphasis on

the experiment suggested in order to measure the

reduction of inertial mass. Computations will be

refined to give a better prediction of the performance

of the proposed propulsion device. Furthermore,

the physical model underlying this propulsion

system will be given a more extensive description.

Acknowledgment

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

Resch, director of IGW at Innsbruck University,

for providing a stimulating working atmosphere

and for numerous discussions concerning Heim's

theory during the last two years.

22 of 26

The authors are very much indebted to Dipl.-

Phys. I. von Ludwiger, former manager and

physicist at DASA, for making available relevant

literature and for many helpful discussions as

well as explanations concerning the implications

of Heim's theory.

The second author was partly funded by Arbeitsgruppe

Innovative Projekte (AGIP), Ministry

of Science and Education, Hanover, Germany.

We are grateful to Prof. Dr. T. Waldeer of the

University of Applied Sciences at Salzgitter

Campus for helpful discussions. The help of T.

Gollnick and O. Rybatzki of the University of

Applied Sciences at Salzgitter Campus in the

preparation of the manuscript is appreciated.

Glossary

aeon Denoting an indefinitely long period of

time. The aeonic dimension can be interpreted

as steering structures governed by the

entelechial dimension toward a dynamically

stable state.

anti-hermetry Coordinates are called anti-hermetric

if they do not deviate from Cartesian

coordinates, i.e., in a space with anti-hermetric

coordinates no physical events can

take place.

condensation For matter to exist, as we are

used to conceive it, a distortion from Euclidean

metric or condensation, a term used by

Heim, is a necessary but not a sufficient condition.

condensor The Christoffel symbols ¤

k m

i become

the so called condensor functions, ¤i

, that are normalizable. This denotation is derived

from the fact that these functions represent

condensations of spacetime metric. A

condensor corresponds to a physical force.

coupling constant Value for creation and destruction

of messenger (virtual) particles,

relative to the strong force (whose value is

set to 1 in relation to the other coupling constants).

coupling potential (Kopplungspotential) The

coupling potential is the first term of the

metric in Eq. (12), denoted as gi k

¤ gp¤ . The

reason for using the superscript gp is that

this part of the photon metric equals the metric

for the gravitophoton particle and that a

sieve (conversion) operator exists, which can

transform a photon into a gravitophoton by

making the second term in the metric antihermetric.

In other words, the electromagnetic

force can be transformed into a gravitational

like force, and thus can be used to reduce

the inertial mass of a material body.

cosmogony (Kosmogonie) The creation or origin

of the world or universe, a theory of the

origin of the universe (derived from the two

Greek words kosmos (harmonious universe)

and gonos (offspring)).

entelechy (Greek entelécheia, objective, completion)

used by Aristotle in his work The

Physics. Aristotle assumed that each phenomenon

in nature contained an intrinsic objective,

governing the actualization of a

form-giving cause. The entelechial dimension

can be interpreted as a measure of the quality

of time varying organizational structures (inverse

to entropy, e.g., plant growth) while

the aeonic dimension is steering these structures

toward a dynamically stable state. Any

coordinates outside spacetime can be considered

as steering coordinates.

eschatology Concerned with the final events in

the history of the universe.

fundamental kernel (Fundamentalkern) Since

the function ¤

i m

¤ ¤¤ occurs in

¤ ¤¤=∫¤i m

¤ ¤¤ d ¤i

as the kernel in the integral,

it is denoted as fundamental kernel of

the poly-metric.

23 of 26

geodesic zero-line process This is a process

where the square of the length element in a

6- or 8-dimensional Heim space is zero.

gravitational limit(s) There are three distances

at which the gravitational force is zero. First,

at any distance smaller than R_, the gravitational

force is 0. Second,

gravitophoton field Denotes a gravitational like

field, represented by the metric sub-tensor,

g i k

¤ gp¤ , generated by a neutral mass with a

smaller coupling constant than the one for

gravitons, but allowing for the possibility

that photons are transformed into gravitophotons.

This field can be used to reduce the

gravitational potential around a spacecraft.

graviton (Graviton) The virtual particle responsible

for gravitational interaction.

Heim-Lorentz force Resulting from the newly

predicted gravitophoton particle that is a

consequence of the Heim space ℝ8. A metric

subtensor is constructed in the subspace

of coordinates I2, S2 and T1, denoted as hermetry

form H5, see [1, 5, 6]. The equation

describing the Heim-Lorentz force has a

form similar to the electromagnetic Lorentz

force, except, that it exercises a force on a

moving body of mass m, while the Lorentz

force acts upon moving charged particles

only. In other words, there seems to exist a

direct coupling between matter and electromagnetism.

In that respect, matter can be

considered playing the role of charge in the

Heim-Lorentz equation. The force is given

by w F

gp=¤

e ¤0

vT× H . Here Λp is a coefficient,

v the velocity of a rotating body (insulator)

of mass m, and H is the magnetic field

strength. It should be noted that the gravitophoton

force is 0, if velocity and magnetic

field strength are perpendicular. Thus, any

experiment that places a rotating disk in a

uniform magnetic field that is oriented parallel

or anti-parallel to the axis of rotation of

this disk, will measure no effect.

hermetry form (Hermetrieform) The word

hermetry is an abbreviation of hermeneutics,

in our case the semantic interpretation of the

metric. To explain the concept of a hermetry

form, the space ℝ6 is considered. There are 3

coordinate groups in this space, namely

s3=¤¤1 ,¤2 ,¤3¤ forming the physical space

ℝ3, s2=¤¤4 ¤ for space T1, and

s1=¤¤5 ,¤6¤ for space S2. The set of all

possible coordinate groups is denoted by

S={s1, s2, s3}. These 3 groups may be combined,

but, as a general rule (stated here

without proof, derived, however, by Heim

from conservation laws in ℝ6

, (see p. 193 in

[2])), coordinates ¤5 and ¤6 must always be

curvilinear, and must be present in all metric

combinations. An allowable combination of

coordinate groups is termed hermetry form,

responsible for a physical field or interaction

particle, and denoted by H. H is sometimes

annotated with an index, or sometimes written

in the form H=(¤1, ¤2 ,...) where ¤1, ¤2 ,...

∈ S. This is a symbolic notation only, and

should not be confused with the notation of

an n-tuple. From the above it is clear that

only 4 hermetry forms are possible in ℝ6. A

6 space only contains gravitation and electrodynamics.

It needs a Heim space ℝ8 to incorporate

all known physical interactions.

Hermetry means that only those coordinates

occurring in the hermetry form are curvilinear,

all other coordinates remain Cartesian.

In other words, H denotes the subspace in

which physical events can take place, since

these coordinates are non-euclidean. This

concept is at the heart of Heim's geometrization

of all physical interactions, and serves as

the correspondence principle between geometry

and physics.

hermeneutics (Hermeneutik) The study of the

methodological principles of interpreting the

metric tensor and the eigenvalue vector of

the subspaces. This semantic interpretation

24 of 26

of geometrical structure is called hermeneutics

(from the Greek word to interpret).

hermitian matrix (self adjoint, selbstadjungiert)

A square matrix having the property

that each pair of elements in the i-th row

and j-th column and in the j-th row and i-th

column are conjugate complex numbers (i ¤

- i). Let A denote a square matrix and A* denoting

the complex conjugate matrix. A† :=

(A*)T = A for a hermitian matrix. A hermitian

matrix has real eigenvalues. If A is real, the

hermitian requirement is replaced by a requirement

of symmetry, i.e., the transposed

matrix AT = A .

homogeneous The universe is everywhere uniform

and isotropic or, in other words, is of

uniform structure or composition throughout.

inertial transformation (Trägheitstransformation)

Such a transformation, fundamentally

an interaction between electromagnetism and

the gravitational like gravitophoton field, reduces

the inertial mass of a material object

using electromagnetic radiation at specific

frequencies. As a result of momentum and

energy conservation in 4-dimensional spacetime,

v/c = v'/c', the Lorentz matrix remains

unchanged. It follows that c < c' and v < v'

where v and v' denote the velocities of the

test body before and after the inertial transformation,

and c and c' denote the speeds of

light, respectively. In other words, since c is

the vacuum speed of light, an inertial transformation

allows for superluminal speeds.

An inertial transformation is possible only in

a 8-dimensional Heim space, and is in accordance

with the laws of SRT. In an Einsteinian

universe that is 4-dimensional and contains

only gravitation, this transformation

does not exist.

isotropic The universe is the same in all directions,

for instance, as velocity of light transmission

is concerned measuring the same

values along axes in all directions.

partial structure (Partialstruktur) For instance,

in ℝ6, the metric tensor that is hermitian

comprises three non-hermitian metrics

from subspaces of ℝ6. These metrics from

subspaces are termed partial structure.

poly-metric The term poly-metric is used with

respect to the composite nature of the metric

tensor in 8D Heim space. In addition, there

is the twofold mapping ℝ4 → ℝ8→ ℝ4.

quantized bang According to Heim, the universe

did not evolve from a hot big bang, but

instead, spacetime was discretized from the

very beginning, and such no infinitely small

or infinitely dense space existed. Instead,

when the size of a single Metron covered the

whole (spherical volume) universe, this was

considered the beginning of this physical universe.

That condition can be considered as

the mathematical initial condition and, when

inserted into Heim's equation for the evolution

of the universe, does result in the initial

diameter of the original universe [1]. Much

later, when the Metron size had decreased

far enough, did matter come into existence

as a purely geometrical phenomenon.

transformation operator or sieve operator

(Sieboperator) The direct translation of

Heim's terminology would be sieve-selector.

A transformation operator, however, converts

a photon into a gravitophoton by making

the coordinate ¤4 Euclidean.

unitary matrix (unitär) Let A denote a square

matrix, and A* denoting the complex conjugate

matrix. If A† := (A*)T = A-1, then A is a

unitary matrix, representing the generalization

of the concept of orthogonal matrix. If

A is real, the unitary requirement is replaced

by a requirement of orthogonality, i.e., A-1 =

AT. The product of two unitary matrices is

unitary.

25 of 26

REFERENCES

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

Space Transportation based on Heim's Field

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

Conference & Exhibit, Indianapolis, Indiana,

7-10 July, 2002, AIAA 2002-2094, 21 pp., see also

www.cle.de/hpcc and www.uibk.ac.at/c/cb/cb26.

2. Millis. M.G.: (ed.), NASA Breakthrough Propulsion

Physics, Workshop Proceedings, NASA/CP-1999

-208694.

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

Beschreibung der Elementarteilchen, Zeitschrift

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

4. Penrose, R.: The Small, the Large and the Human

Mind, Cambridge University Press, 1997.

5. Heim, B.: Elementarstrukturen der Materie, Band 1,

Resch Verlag, 2nd ed., Innsbruck, 1989.

6. Heim, B.: Elementarstrukturen der Materie, Band 2,

Resch Verlag, Innsbruck, 1984.

7. Heim, B. and W. Dröscher: Strukturen der physikalischen

Welt und ihrer nichtmateriellen Seite, Innsbruck,

Resch Verlag, 1996.

8. Guth, A. and P. Steinhardt: The inflationary Universe

in The New Physics, ed. P. Davies, Cambridge Press,

1991.

9. Silk, J.: The Big Bang, Cambridge University Press,

2000.

10. Mbelek, J.P. , M. Lachièze-Rey: Possible Evidence

from Laboratory Measurements for a Latidute and

Longitude Dependence of G, arXiv:gr-qc/0204064, 19

April 20002.

11. Mbelek, J.P. , M. Lachièze-Rey: A five dimensional

Model of Varying Effective Gravitational and Fine

Structure Constants, arXiv:gr-qc/0205089, 14 October

20002.

12. Vladimirov,Y. et al.: Space, Time, Gravitation, Mir

Publishers, 1987.

13. Cline, D.B.: The Search for Dark Matter, Scientific

American, February 2003.

14. Lawrie, I.D.: A Unified Grand Tour of Theoretical

Physics, 2nd ed., IoP 2002.

15.Tajmar, M.: Advanced Space Transportation, Springer,

2003.

16. World Spaceflight News, 21th Century and Beyond,

Future Space Rockets and Breakthrough Propulsion.

17. Harris, E.G.: Modern Theoretical Physics, Vol I,

Wiley&Sons, 1975.

18. Kiefer, C., Lämmerzahl, C.: Breitet sich die Gravitation

mit Lichgeschwindigkeit aus, Physik Journal,

March 2003 and Will, C., astro-ph/0301145.

19. Zubrin, R.: Entering Space, Putnam, 2000.

20. Forward, R. L., Advanced Propulsion Systems,

Chap.11 in Space Propulsion Analysis and Design,

eds. R. W. Humble et al., McGrawHill, 1995.

21. Fortagh, J, Zimmermann, C., Bose-Einstein Kondensate

in magnetischen Mikrofallen, Physik Journal,

June 2003 and Fortag, J., Physical Review A66,

041604(R), 2002.

22. Chaisson, E., McMillan, S., Astronomy Today, Chap.

22.2, 4th ed., Prentice Hall, 2002.

23. Purcell, E.M., Electricity and Magnetism, Chap. 10,

Vol II Berkeley Physics Course, McGrawHill, 2nd ed.,

1983.

24. Serway, R., Physics, p. 884, 4th ed., Saunders, 1996.

25. Woan, G., The Cambridge Handbook of Physics Formulas,

Cambridge Univ. Press, 2000.

26.Tipler, P.A., Llewellyn, R.A., Modern Physics,

Chap.13, Freeman 1999.

27 Landau, L., Lifschitz, E., Lehrbuch der Theoretischen

Physik, Volume IV, 1991.

26 of 26

aiaa2003-4990-letter.pdf (1,3 MB)

Tags:

Back

AIAA 2003-4990 FUTURE SPACE PROPULSION BASED ON HEIM'S FIELD THEORY

Tags:

Search site

Contact