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SAROD-2005

1 PHYSICAL PRINCIPLES FOR

PROPULSION SYSTEMS†‡*

All propulsion systems in use today are based on

momentum conservation and rely on fuel [1]. There is one

exception, namely gravity assist turns that use the

gravitational fields of planets to accelerate a spacecraft.

The only other long-range force known is the

electromagnetic force or Lorentz force, acting on charged

bodies or moving charges. Magnetic fields around planets

or in interstellar space are too weak to be used as a means

for propulsion. In the solar system and in the universe as

known today, large-scale electromagnetic fields that

could accelerate a space vehicle do not seem to exist.

However, magnetic and electric fields can easily be

generated, and numerous mechanisms can be devised to

produce ions and electrons and to accelerate charged

particles. The field of magnetohydrodynamics recently

has become again an area of intensive research, since

†University of Applied Sciences and HPCC-Space GmbH,

Salzgitter, Germany

# IGW, Leopold-Franzens University, Innsbruck, Austria

‡ Aerodynamisches Institut, RWTH Aachen, Germany

* ESA-ESTEC, Noordwijk, The Netherlands

© J. Häuser, Walter Dröscher

SAROD-2005

Published in 2005 by Tata McGraw-Hill

both high-performance computing, allowing the

simulation of these equations for realistic two- and three-

dimensional configurations, and the progress in

generating strong magnetic and electric fields have

become a reality. Although the main physical ideas of

MHD were developed in the fifties of the last century, the

actual design of efficient and effective propulsion systems

only recently became possible.

One weakness that all concepts of propulsion have in

common today is their relatively low thrust. An analysis

shows that only chemical propulsion can provide the

necessary thrust to launch a spacecraft. Neither fission

nor fusion propulsion will provide this capability. MHD

propulsion is superior for long mission durations, but

delivers only small amounts of thrust. Space flight with

current propulsion technology is highly complex, and

severely limited with respect to payload capability,

reusability, maintainability. Above all it is not

economical. In addition, flight speeds are marginal with

respect to the speed of light. Moreover, trying only to fly

a spacecraft of mass 105 kg at one per cent (non-

relativistic) the speed of light is prohibitive with regard to

the kinetic energy to be supplied. To reach velocities

comparable to the speed of light, special relativity

imposes a heavy penalty in form of increasing mass of

the spacecraft, and renders such an attempt completely

uneconomical.

The question therefore arises whether other forces

(interactions) in physics exist, apart from the four known

Physical and Numerical Modeling for

Advanced Propulsion Systems

Jochem Hauser †# Walter Dröscher# Wuye Dai‡ Jean-Marie Muylaert*

Abstract

The paper discusses the current status of space transportation and then presents an overview of the two main

research topics on advanced propulsion as pursued by the authors, namely the use of electromagnetic interaction

(Lorentz force) as well as a novel concept, based on ideas of a unified theory by the late German physicist B.

Heim, termed field propulsion. In general, electromagnetics is coupled to the Navier-Stokes equations and leads

to magnetohydrodynamics (MHD). Consequently, the ideal MHD equations and their numerical solution based

on an extended version of the HLLC (Harten-Lax-van Leer-Contact discontinuity) technique is presented. In

particular, the phenomenon of waves in MHD is discussed, which is crucial for a successful numerical scheme.

Furthermore, the important topic of a numerically divergence free magnetic induction field is addressed. Two-

dimensional simulation examples are presented. In the second part, a brief discussion of field propulsion is given.

Based on Einstein's principle of geometrization of physical interactions, a theory is presented that shows that

there should be six fundamental physical interactions instead of the four known ones. The additional interactions

(gravitophoton force) would allow the conversion of electromagnetic energy into gravitational energy where the

vacuum state provides the interaction particles. This kind of propulsion principle is not based on the momentum

principle and would not require any fuel. The paper discusses the source of the two predicted interactions, the

concept of parallel space (in which the limiting speed of light is nc, n being an integer, c denoting vacuum speed

of light), and presents a brief introduction of the physical model along with an experimental setup to measure and

estimate the so called gravitophoton (Heim-Lorentz) force. Estimates for the magnitude of magnetic fields are

presented, and trip times for lunar and Mars missions are given.

Key Words: physical principles of advanced propulsion, electromagnetic propulsion, numerical solution of the MHD

equations; field propulsion, six fundamental physical interactions, conversion of electromagnetic energy into

gravitational energy, Heim-Lorentz force.

2 Jochem Hauser , Walter Dröscher, Wuye Dai, and Jean-Marie Muylaert

interactions in Nature, namely long-range gravitational

and electromagnetic interactions, and on the nuclear scale

the weak (radioactive decay, neutron decay is an

example) and strong interactions (responsible for the

existence of nuclei)? It has long been surmised that,

because of their similarity, electromagnetic fields can be

converted into gravitational fields. The limits of

momentum based propulsion as enforced by governing

physical laws, are too severe, even for the more advanced

concepts like fusion and antimatter propulsion, photon

drives and solar and magnetic sails. Current physics does

not provide a propulsion principle that allows a lunar

mission to be completed within hours or a mission to

Mars within days. Neither is there a possibility to reach

relativistic speeds (at reasonable cost and safety) nor are

superluminal velocities conceivable. As mentioned by

Krauss [2], general relativity (GR) allows metric

engineering, including the so-called Warp Drive, but

superluminal travel would require negative energy

densities. However, in order to tell space to contract

(warp), a signal is necessary that, in turn, can travel only

with the speed of light. GR therefore does not allow this

kind of travel.

On the other hand, current physics is far from providing

final answers. First, there is no unified theory that

combines general relativity (GR) and quantum theory

(QT) [3-6]. Second, not even the question about the

number of fundamental interactions can be answered.

Currently, four interactions are known, but theory cannot

make any predictions on the number of existing

interactions. Quantum numbers, characterizing

elementary particles (EP) are introduced ad hoc. The

nature of matter is unknown. In EP physics, EPs are

assumed to be point-like particles, which is in clear

contradiction to recent lopp quantum theory (LQT) [3, 4]

that predicts a granular space, i.e., there exists a smallest

elemental surface. This finding, however, is also in

contradiction with string theory (ST) [5, 6] that uses

point-like particle in ℝ4 but needs 6 or 7 additional real

dimensions that are compactified (invisible, Planck

length). Neither LQT nor ST predict measurable physical

effects to verify the theory.

Most obvious in current physics is the failure to predict

highly organized structures. According to the second law

of thermodynamics these structures should not exist. In

cosmology the big bang picture requires the universe to

be created form a point-like infinitely dense quantity that

defies any logic. According to Penrose [7] the probability

for this to happen is zero. Neither the mass spectrum nor

the lifetimes of existing EPs can be predicted. It therefore

can be concluded that despite all the advances in

theoretical physics, the major questions still cannot be

answered. Hence, the goal to find a unified field theory is

a viable undertaking, because it might lead to novel

physics [8], which, in turn, might allow for a totally

different principle in space transportation.

2 MAGNETO-HDYRODYNAMIC

PROPULSION

Because of the inherent limitations of chemical

propulsion to deliver a specific impulse better than 450 s,

research concentrated on electromagnetic propulsion

already in the beginning of the space flight area, i.e., in

the fifties of the last century. Electric and plasma

propulsion systems were designed and tested some 35

years ago, but until recently have not made a contribution

to the problem of space transportation. Allowing for a

much higher specific impulse of up to 104 s, the total

thrust delivered by a plasma propulsion system is

typically around 1 N and some 20 mN for ion propulsion.

No payload can be lifted form the surface of the earth

with this kind of propulsion system. On the other hand,

operation times can be weeks or even months, and

interplanetary travel time can be substantially reduced. In

addition, spacecraft attitude control can be maintained for

years via electric propulsion.

2.1 MHD Equations

The MHD equations are derived from the combination of

fluid dynamics (mass, momentum, and energy

conservation) and Maxwell equations. In addition,

generalized Ohm's law,

j= ev×B,

is used and

displacement current

∂E/ ∂t

in Ampere's law is

neglected. The curl of E in farady's law is replaced by

taking the curl of j and inserting it into Faraday's law.

Making use of the identity

∇×∇ ×B=−∇2B,

with

∇⋅B=0,

one obtains the equation for the B field.

Introducing the magnetic Reynolds number

Rem=vL/ m,m=1

0,

which denotes the ratio of the

∇×v×B

convection term and the

m∇2B

diffusion term, the ideal MHD equations are obtained

assuming an infinitely high conductivity σ of the

plasma. The MHD equations can thus be written in

conservative form

∂U

∂t∇⋅F=0

(1)

U=

[

v

E

B

]

(2)

F=

[

v

v vPI−B B

EPv−Bv⋅B

v B−B v

]

(3)

where is ρ mass density, v is velocity, and E denotes total

energy. P includes the magnetic pressure B2/2μm.

Physical and Numerical Modeling for Advanced Propulsion Systems 3

E=p/−1u2v2w2/2

+Bx

2By

2Bz

2/2m

(4)

P=pBx

2By

2Bz

2/2m.

(5)

In additional to the above equations, the magnetic field

satisfies the divergence free constraint

∇⋅B=0 .

This

is not an evolution equation and has to be satisfied

numerically at each iteration step for any kind of grid.

Special care has to be taken to guarantee that this

condition is satisfied, otherwise the solution may become

non-physical. Due to the coupling of the induction

equation to the momentum and energy equations, these

quantities would also be modeled incorrectly.

2.2 Numerical Solution of the MHD Equations

The above ideal MHD equations constitute a non-strictly

hyperbolic partial differential system. From the analysis

of the governing equations in one-dimensional spatio-

temporal space, proper eigenvector and eigenvalues can

be found. The seven eigenvalues of the MHD equations

are (the details of the MHD waves are presented in [13]):

[u ,u±cA,u±cs,u ±cf].

All velocity component

are in the direction of propagation of the wave.

2.2.1 MHD-HLLC Algorithm

In order to approximate the flux function, the appropriate

Riemann problem is solved on the domain

xl, xr

and

integrated in time from

0 tot f.

A major task is the

evaluation of the wave propagation speeds.

q*=sM=

rqrsr−qr−lqlsl−qlpl−pr−Bnl

2Bnr

2

rsr−qr−lsl−ql

(6)

P*=sl−qq*−qP−Bn

2 Bn

*2.

(7)

In order to evaluate the integrals, the (yet unknown)

signal speeds

sland sr

are considered, denoting the

fastest wave propagation in the negative and positive x-

directions. It is assumed, however, that at the final time

tf,

no information has reached the left,

xl0,

and

right,

xr0,

boundaries of the spatial integration

interval that is,

xlsltf and xrsrtf.

Applying the

Rankine-Hugoniot jump conditions to the ideal MHD

equations and observing a conservation principle for the

B field, eventually leads to

K

*=K

SK−qK

SK−q*

uK

*= uK

SK−qK

SK−q*+

P*−PKnxBnK BxK−B*Bx

*

SK−q*¿

vK

*= vK

SK−qK

SK−q*+

P*−PKnyBnK ByK−B*By

*

SK−q*

EK

*=EK

SK−qK

SK−q*+

P*q*−PKqKBnK B⋅vK−B*B⋅v*

SK−q*

(8)

(9)

Byl

*=Byr

*=By

HLL

,

Bzl

*=Bzr

*=Bz

HLL

(10)

(11)

2.2.2 Wavespeed Computation

The eigenvalues reflect four different wave speeds for a

perturbation propagating in a plasma field: the usual

acoustic, the Alfven as well as the slow and fast plasma

waves

a2= ∂p

∂

s

(12)

cA

2=Bn

2/ m

(13)

2cs , f

2=a2B2

m

±

a2B2

m

2

−4a2cA

2.

(14)

FHLLC=

{

Flif 0sl

Fl

*=FlslUl

*−Ulif sl≤0≤q*

Fr=FrsrUr

*−Ur*if q*≤0≤sr

Frif sr0

}

.

Bxl

*=Bxr

*=Bx

HLL=srBxr −slBxl

sr−sl

4 Jochem Hauser , Walter Dröscher, Wuye Dai, and Jean-Marie Muylaert

2.2.3 Divergence Free B Field

To obtain a divergence free induction field in time, a

numerical scheme for the integration of the B filed has to

be constructed that inherenltly satisfies this constraint

numerically. The original equations should not be

modified, neither should an additional Poisson equation

be solved at each iteration step to enforce a divergence

free B field. For the lack of space we refer to Torrilhon

[14] or to [13]. In 2D where the vector potentia lonly has

a z-component, the divergence of B only depends on

components Bx and By. the magnetic field is defined at

two locations: at the center of the computational cells, and

at the surfaces. In fact, only the normal component is

defined at the cell surfaces (the magnetic flux), for a

Cartesian grid. The evolution of the magnetic field at the

cell surface is then obtained by directly solving the

Ampere equation. Defining

=v×B

at cell vertices, it

can be shown [14] that the field at the cell surface centers

can be obtained in such a way that the divergence-free

condition is exactly satisfied.

∂b

∂t=∇×⇒

{

∂bx

∂t=∇ yz

∂by

∂t=∇ xz

}

(15)

bx ,i1/2, j=

t

y[z , i1/2, j1/2−z ,i1/2, j−1/2]

by ,i , j1/2=

- t

y[z , i1/2, j1/2−z ,i−1/2, j1/2]

(16)

∮b⋅dS=0⇒ y[bx ,i1/2, j−bx, i−1/2, j]

x[by ,i , j1/2−by , i , j−1/2]=0

(17)

Bxi , j =1

2[bx ,i1/2, jbx , i−1/2, j]

Byi , j=1

2[by ,i , j 1/2by ,i , j −1/2]

(18)

Figure 1: Schematic of staggered-grid variables used in the

Dai & Woodward scheme. For a non-orthogonal

coordinates a staggered grid does not seem to have an

advantage, since cell normal vectors do no longer point in a

coordinate direction. A cell centered scheme seems to be

advantageous for curvilinear coordinates.

2.3 Simulation Results

2.3.1 Brio-Wu's shock tube

Initial conditions:

=2.0, V=0, Bz=0, Bx=0.75

=1, p=1, by=1 for x0

=0.125, p=0.1, By=−1 for x≥0

Computational domain is the rectangle [-1,1].

2.3.2 Supersonic Flow Past Circular Density Field

The solution domain is in the x-y plane [-1.5, 3.5; -4.0,

4.0], example first computed by M. Torrilhon.

Figure 2: 1D MHD solution at time t = 0.25s.

Physical and Numerical Modeling for Advanced Propulsion Systems 5

Initial conditions: outside the density sphere, velocity

component vx=3,

=1.

Inside the density sphere:

=10,

velocity vx=0. For all: B=(Bx=B0, 0), p = 1,

vy=0 and

=5/3 .

Figure 3: Supersonic flow past initial density field, shown

pressure distributions: left: B0=0, right B0=1. The impact

of the magnetic induction on the pressure distribution is

clearly visible.

2.3.3 Classic 2D MHD Orszag-Tang Vortex

Computation domain is a square domain of size

[0, 2]×[0, 2 ].

Initial conditions are given by:

vx, v y=−sin y ,sin x

Bx, B y=−sin y ,sin 2x

, p , v z, Bz= 25 /9,5/3 ,0 ,0 with =5/3

This case uses periodic boundary conditions.

Figure 5: Orszag–Tang MHD turbulence problem with a

384 × 384 uniform grid at t=2s.

3 FIELD PROPULSION

The above discussion has shown that current physical

laws severely limit spaceflight. The German physicist, B.

Heim, in the fifties and sixties of the last century

developed a unified field theory based on the

geometrization principle of Einstein 18 (see below)

introducing the concept of a quantized spacetime but

using the equations of GR and introducing QMs. A

quantized spacetime has recently been used in quantum

gravity. Heim went beyond general relativity and asked

the question: if the effects of the gravitational field can be

described by a connection (Christoffel symbols) in

spacetime that describes the relative orientation between

local coordinate frames in spacetime, can all other forces

of nature such as electromagnetism, the weak force, and

the strong force be associated with respective connections

or an equivalent metric tensor. Clearly, this must lead to a

higher dimensional space, since in GR spacetime gives

rise to only one interaction, which is gravity.

Figure 4: Orszag–Tang MHD turbulence problem with a

384 × 384 uniform grid at t=2s.

6 Jochem Hauser , Walter Dröscher, Wuye Dai, and Jean-Marie Muylaert

The fundamental difference to GR is the existence of

internal space H 8, and its influence on and steering of

events in ℝ4. In GR there exists only one metric leading

to gravity. All other interactions cannot be described by a

metric in ℝ4. In contrast, since internal symmetry space is

steering events in ℝ4, the following (double) mapping,

namely ℝ4H8ℝ4, has to replace the usual mapping

ℝ4ℝ4 of GR. This double mapping is the source of the

polymetric describing all physical interactions that can

exist in Nature. The coordinate structure of H8 is therefore

crucial for the physical character of the unified field

theory. This structure needs to be established from basic

physical features and follows directly from the physical

principles of Nature (geometrization, optimization,

dualization (duality), and quantization). Once the

structure of H8 is known, a prediction of the number and

nature of all physical interactions is possible.

As long as quantization of spacetime is not considered,

both internal symmetry space, denoted as Heim space H

8, and spacetime of GR can be conceived as manifolds

with metrics.

3.1 Six Fundamental Interactions

Einstein, in 1950 [9], emphasized the principle of

geometrization of all physical interactions. The

importance of GR is that there exists no background

coordinate system. Therefore, conventional quantum field

theories that are relying on such a background space will

not be successful in constructing a quantum theory of

gravity. In how far string theory [5, 6], ST, that uses a

background metric will be able to recover background

independence is something that seems undecided at

present. On the contrary, according to Einstein, one

should start with GR and incorporate the quantum

principle. This is the approach followed by Heim and also

by Rovelli, Smolin and Ashtekar et al. [3, 4]. In addition,

spacetime in these theories is discrete. It is known that the

general theory of relativity (GR) in a 4-dimensional

spacetime delivers one possible physical 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. Everywhere highly evolved structures

can be seen, which is an enigma for the science of today.

Consequently, the theory utilizes an entelechial

dimension, x5, an aeonic dimension, x6 (see glossary), and

coordinates x7, x8 describing information, i.e., quantum

mechanics, resulting in an 8-dimensional discrete space in

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

exists. H8 comprises real fields, the hermetry forms,

producing real physical effects. One of these hermetry

forms, H1, is responsible for gravity, but there are 11

other hermetry forms (partial metric) plus 3 degenerated

hermetry forms, part of them listed in Table 2. The

physics in Heim theory (HT) is therefore determined by

the polymetric of the hermetry forms. This kind of poly-

metric is currently not included in quantum field theory,

loop quantum gravity, or string theory.

3.2 Hermetry Forms and Physical Interactions

In this paper we present the physical ideas of the

geometrization concept underlying Heim theory in 8D

space using a series of pictures, see Figs. 6-8. The

mathematical derivation for hermetry forms was given in

[10-12]. As described in [10] there is a general coordinate

transformation

xm i

from ℝ4H8ℝ4 resulting

in the metric tensor

gi k =∂xm

∂

∂

∂i

∂xm

∂

∂

∂k

(19)

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.

gi k =:∑

,=1

8

gi k

(20)

gi k

=∂xm

∂

∂

∂i

∂xm

∂

∂

∂k.

(21)

Twelve hermetry forms can be generated having direct

physical meaning, by constructing specific combinations

from the four subspaces. The following denotation for the

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

used:

gi k Hℓ=:∑

, ∈ Hℓ

gi k

(22)

where summation indices are obtained from the definition

of the hermetry forms. The expressions

gi k Hℓ

are

interpreted as different physical interaction potentials

caused by hermetry form Hℓ, extending the interpretation

of metric employed in GR to the poly-metric of H8. It

should be noted that any valid hermetry form either must

contain space S2 or I2.

Each individual hermetry form is equivalent to a physical

potential or a messenger particle. It should be noted that

spaces S2×I2 describe gravitophotons and S2×I2×T1 are

responsible for photons. There are three, so called

degenerated hermetry form describing neutrinos and so

called conversions fields. Thus a total of 15 hermetry

forms exists.

Physical and Numerical Modeling for Advanced Propulsion Systems 7

In Heim space there are four additional internal

coordinates with timelike (negative) signature, giving rise

to two additional subspaces S2 and I2. Hence, H8

comprises four subspaces, namely ℝ3, T1, S2, and I2. The

picture shows the kind of metric-subspace that can be

constructed, where each element is denoted as a hermetry

form. Each hermetry form has a direct physical meaning,

see Table 3. In order to construct a hermetry form, either

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

are two degenerated hermetry forms that describe partial

forms of the photon and the quintessence potential. They

allow the conversion of photons into gravitophotons as

well as of gravitophotons and gravitons into

quintessence particles.

There are two equations describing the conversion of

photons into pairs of gravitophotons, Eqs. (23), for details

see [10-12]. The first equation describes the production of

N2 gravitophoton particles from photons.

wph r−wph=Nwgp

wph r−wph=Awph .

(23)

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's

radiation correction. Conversion amplitude: The physical

meaning of Eqs. (23) is that an electromagnetic potential

(photon) containing probability amplitude Awph can be

converted into a gravitophoton potential with amplitude

Nwgp,, see Eq. (24).

Nwgp=Aw ph .

(24)

In the rotating torus, see Fig. 9, virtual electrons are

produced by the vacuum, partially shielding the proton

charge of the nuclei. At a distance smaller than the

Compton wavelength of the electron away from the

nucleus, the proton charge increases, since it is less

shielded. According to Eq. (24) a value of A larger than 0

is needed for gravitophoton production. As was shown in

[10], however, a smaller value of A is needed to start

converting photons into gravitophotons to make the

photon metric vanish, termed

A=vkvk

T/c2≈10−11

where v is the velocity of the electrons in the current loop

and vT is the circumferential speed of the torus. From the

vanishing photon metric, the metric of the gravitophoton

Figure 6: Einstein's goal was the unification of all

physical interactions based on his principle of

geometrization, i.e., having a metric that is responsible for

the interaction. This principle is termed Einstein's

geometrization principle of physics (EGP). To this end,

Heim and Dröscher introduced the concept of an internal

space, denoted as Heim space H8, having 8 dimensions.

Although H8 is not a physical space, the signature of the

additional coordinates being timelike (negative), these

invisible internal coordinates govern events in spacetime .

Therefore, a mapping from manifold M (curvilinear

coordinates ηl )in spacetime ℝ4 to internal space H8 and

back to ℝ4 .

MH8N

4

H8

4

l1, . . . , 4

curvilinear

1, . . . , 8

Heim space Euclidean

m1, . . . , 4

l

xm

gik

Heim Polymetric

gik

Figure 8: There should be three gravitational particles,

namely the graviton (attractive), the gravitophoton

(attractive and repulsive), and the quintessenece or

vacuum particle (repulsive), represented by hermetry

forms H1, H5, and H9, see Table 2.

conversion

Figure 7: The picture shows the 12 hermetry forms that

can be constructed from the four subspaces, nalely

namely ℝ3, T1, S2, and I2 (see text).

H8

S2

S2I2

I2

gik

9

3

gik

10

T1

gik

11

3T1

gik

12

gik

1

3

gik

2

T1

gik

3

3T1

gik

4

gik

5

3

gik

6

T1

gik

7

3T1

gik

8

Heim Space

In H8, there exists 12 subspaces, whose metric gives

6 fundamental interactions

(+ + + - - - - -)

signature of H8

8 Jochem Hauser , Walter Dröscher, Wuye Dai, and Jean-Marie Muylaert

pairs is generated, replacing the value of A by the LHS of

Eq. (6) and inserting it into the equation for the

gravitophoton metric. This value is then increased to the

value of A in Eq.(6). Experimentally this is achieved by

the current loop (magnetic coil) that generates the

magnetic vector and the tensor potential at the location of

the virtual electron in the rotating torus, producing a high

enough product v vT, see Eq. 32 in [12]. The coupling

constants of the two gravitophoton particles are different,

and only the negative (attractive) gravitophotons are

absorbed by protons and neutrons, while absorption by

electrons can be neglected. This is 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 (see upper part of the picture).

3.3 Gravitational Heim-Lorentz Force

The Heim-Lorentz force derived in [10-12] is the basis

for the field propulsion mechanism. In this section a

description of the physical processes for the generation

of the Heim-Lorentz force is presented along with the

experimental setup. It turns out that several conditions

need to be satisfied. In particular, very high magnetic

field strengths are required.

In Table 1, the magnitude of the Heim-Lorentz force is

given. The current density is 600 A/mm2. The value Δ is

the relative change with respect to earth acceleration

g=9.81 m/s2 that can be achieved at the corresponding

magnetic field strength. The value μ0H is the magnetic

induction generate by the superconductor at the location

of the rotating torus, D is the major diameter of the torus,

while d is the minor diameter. In stands for the product of

current and times the number of turns of the magnetic

coil. The velocity of the torus was assumed to be 700 m/s.

Total wire length would be some 106 m. Assuming a

reduction in voltage of 1μV/cm for a superconductor, a

thermal power of some 8 kW has to be managed. In

general, a factor of 500 needs to be applied at 4.2 K to

calculate the cooling power that amounts to some 4 MW.

32

3

Nwgpe

wph

2

Nwgpa

4

ℏ

mpc

2d

d0

3Z.

(25)

d

[m]

D

[m]

I n

[An]

N w gpe

0H

(T)

0.2 2 6.6 ×1061.4× 10-7 13 7×10-16

0.3 3 1.3 ×1077.4 ×10-6 18 2×10-5

0.4 4 2.7 ×107 2×10-5 27 1.1×10-2

0.5 5 4 ×1073.9×10-5 33 0.72

0.6 6 1.5 ×1074.8×10-5 38 3

Table 1: From the Heim-Lorentz force the following

values are obtained. A mass of 1,000 kg of the torus is

assumed, filled with 5 kg of hydrogen.

3.4 Transition into Parallel Space

Under the assumption that the gravitational potential of

the spacecraft can be reduced by the production of

quintessence particles as discussed in Sec.1., a transition

into parallel space is postulated to avoid a potential

conflict with relativity theory. A parallel space ℝ4(n), in

which covariant physical laws with respect to ℝ4 exist, is

characterized by the scaling transformation

xin= 1

n2x1, i =1,2,3 ; t n= 1

n3t 1

vn=n v 1; cn=n c1

Gn=1

nG ; ℏn =ℏ ; n ∈ℕ.

(26)

The fact that n must be an integer stems from the

requirement in HQT and LQT for a smallest length scale.

Hence only discrete and no continuous transformations

are possible. The Lorentz transformation is invariant with

regard to the transformations of Eqs. (26) 1. In other

words, physical laws should be covariant under discrete

(quantized) spacetime dilatations (contractions). There are

1 It is straightforward to show that Einstein's field

equations as well as the Friedmann equations are also

invariant under dilatations.

Figure 9: This picture shows the experimental setup to

measuring the Heim-Lorentz force. The current loop

(blue) provides an inhomogeneous magnetic field at the

location of the rotating torus (red). The radial field

component causes a gradient in the z-direction (vertical).

The red ring is a rotating torus. The experimental setup

also would serve as the field propulsion system, if

appropriately dimensioned. For very high magnetic fields

over 30 T, the current loop or solenoid must be

mechanically reinforced because of the Lorentz force

acting on the moving electrons in the solenoid, forcing

them toward the center of the loop.

I

N

B

r

B I

r

Physical and Numerical Modeling for Advanced Propulsion Systems 9

two important questions to be addressed, namely how the

value n can be influenced by experimental parameters,

and how the back-transformation from ℝ4(n) ℝ4 is

working. The result of the back-transformation must not

depend on the choice of the origin of the coordinate

system in ℝ4. As a result of the two mappings from ℝ4

ℝ4(n)ℝ4 , the spacecraft has moved a distance n v Δt

when reentering ℝ4. The value Δt denotes the time

difference between leaving and reentering ℝ4, as

measured by an observer in ℝ4. 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 ℝ4, is

not transformed again when going back from ℝ4(n) to ℝ4.

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 ℝ4(n) and thus is being

transformed. The spacecraft is assumed to be leaving ℝ4

with velocity v. Since energy needs to be conserved in

ℝ4, the kinetic energy of the spacecraft remains

unchanged upon reentry.

The value of n is obtained from the following formula,

Eq. (27), relating the field strength of the gravitophoton

field, g+gp, with the gravitational field strength, gg,

produced by the spacecraft itself,

n=ggp

+

gg

Ggp

G.

(27)

For the transition into parallel space, a material with

higher atomic number is needed, here magnesium Mg

with Z=12 is considered, which follows from the

conversion equation for gravitophotons and gravitons into

quintessence particles (stated without proof). Assuming a

value of gg= GM/R2 = 10-7 m/s2 for a mass of 105 kg and a

radius of 10 m, a value of gg= 2 10-5 m/s2 is needed

according to Eq. (27). provided that Mg as a material is

used, a value of (see Table 1) I n =1.3107 is needed. If

hydrogen was used, a magnetic induction of some 61 T

would be needed, which hardly can be reached with

present day technology.

3.5 Mission Analysis Results

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 ×105 kg. With a magnetic induction of 20 T,

compare Table 1 a rotational speed of the torus of vT = 103

m/s, and a torus mass of 2×103 kg, an acceleration larger

than 1g is produced and thus the first half of the distance,

dM, to the moon is covered in some 2 hours, which

follows from

t=

2dM/g,

resulting in a total flight time

of 4 hours. A Mars mission, under the same assumptions

as a flight to the moon, would achieve a final velocity of

v= gt = 1.49×106 m/s. The total flight time to Mars with

acceleration and deceleration is 3.4 days. Entering

parallel space, a transition is possible at a speed of some

3×104 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 [10-12].

4 CONCLUSION

In GR the geometrization of spacetime gives rise to

gravitation. Einstein's geometrization principle was

extended to construct a poly-metric that describes all

known physical interactions and also predicts two

additional like gravitational forces that may be both

attractive and repulsive. In an extended unified theory

based on the ideas of Heim four additional internal

coordinates are introduced that affect events in our

spacetime. Four subspaces can be discerned in this 8D

world. From these four subspaces 12 partial metric

tensors, termed hermetry forms, can be constructed that

have direct physical meaning. Six of these hermetry

forms are identified to be described by Lagrangian

densities and represent fundamental physical

interactions. The theory predicts the conversion of

photons into gravitophotons, denoted as the fifth

fundamental interaction. The sixth fundamental

interaction allows the conversion of gravitophotons

and gravitons (spacecraft) into the repulsive vacuum or

quintessence particles. Because of their repulsive

character, the gravitational potential of the spacecraft

is being reduced, requiring either a reduction of the

gravitational constant or a speed of light larger than the

vacuum speed of light. Both possibilities must be ruled

out if the predictions of LQT and Heim theory are

accepted, concerning the existence of a minimal

surface. That is, spacetime is a quantized (discrete)

field and not continuous. A lower value of G or a

higher value of c clearly violate the concept of minimal

surface. Therefore, in order to resolve this

contradiction, the existence of a parallel space is

postulated in which covariant laws of physics hold, but

fundamental constants are different, see Eq. (11). The

conditions for a transition in such a parallel space are

given in Eq. (12).

It is most interesting to see that the consequent

geometrization of physics, as suggested by Einstein in

1950 [9] starting from GR and incorporating quantum

theory along with the concept of spacetime as a

quantized field as used by Heim and recently in LQT,

leads to major changes in fundamental physics and

would allow to construct a completely different space

propulsion system.

Acknowledgments

The first author is grateful to M. Torrilhon, SAM, ETH

Zurich, Switzerland for discussions concerning both the

implementation of a numerically divergence free

magnetic induction field and of boundary conditions.

This work was partly funded by Arbeitsgruppe Innovative

10 Jochem Hauser , Walter Dröscher, Wuye Dai, and Jean-Marie Muylaert

Projekte (AGIP) and Ministry of Science, Hanover,

Germany under Efre contract.

REFERENCES

[1] Zaehringer, A., Rocket Science, Apogee Books,

2004, Chap 7.

[2] Krauss, L.M., “Propellantless Propulsion: The Most

Inefficient Way to Fly?”, in M. Millis (ed.) NASA

Breakthrough Propulsion Physics Workshop

Proceedings, NASA/CP-1999-208694, January

1999.

[3] Rovelli, C., “Loop Quantum Gravity”, Physics

World, IoP, November 2003.

[4] Smolin, L., “Atoms of Space and Time”, Scientific

American, January 2004.

[5] Zwiebach, R., Introduction to String Theory,

Cambridge Univ. Press, 2004.

[6] Lawrie, I. D., A Unified Grand Tour of Theoretical

Physics, 2nd ed., IoP 2002.

[7] Penrose, R., The Road to Reality, Chaps. 30-32,

Vintage, 2004.

[8] Heim, B., “Vorschlag eines Weges einer

einheitlichen Beschreibung der Elementarteilchen”,

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

[9] Einstein, On the Generalized Theory of Gravitation,

Scientific American, April 1950, Vol 182, NO.4.

[10] Dröscher, W., J. Hauser, AIAA 2004-3700, 40th

AIAA/ASME/SAE/ASE, Joint Propulsion

Conference & Exhibit, Ft. Lauderdale, FL, 7-10

July, 2004, 21 pp., see www.hpcc-space.com .

[11] Dröscher, W., J. Hauser, Heim Quantum Theory for

Space Propulsion Physics, 2nd Symposium on New

Frontiers and Future Concepts, STAIF, American

Institute of Physics, CP 746, Ed. M.S. El-Genk 0-

7354-0230-2/05, 12 pp. 1430-1441, www.hpcc-

space.com .

[12] Dröscher, W., J. Hauser, AIAA 2005-4321, 41th

AIAA/ASME/SAE/ASE, Joint Propulsion

Conference & Exhibit, Tuscon, AZ, 7-10 July, 2005,

12pp., see www.hpcc-space.com .

[13] Hauser, J, W. Dai: Plasma Solver (PS-JUST) for

Magnetohydrodynamic Flow-Java Ultra Simulator

Technology, ESTEC/Contract no 18732/04/NL/DC,

2005.

[14] M. Torrilhon, “Locally Divergence-Preserving

Upwind Finite Volume Schemes for

Magnetohydrodynamic Equations”, SIAM J. Sci.

Comput. Vol. 26, No. 4, pp. 1166-1191, 2005.

Table 2: The hermetry forms for the six fundamental physical interactions.

Subspace Hermetry form

Lagrange density

Messenger particle Symmetry

group

Physical

interaction

S2

H1S2, LG

graviton U(1) gravity +

S2×I2

H5S2×I2, Lgp

− neutral

three types of

gravitophotons

U(1)× U(1) gravitation + −

vacuum field

S2×I2×ℝ3

H6S2×I2×ℝ3, Lew

Z0

boson SU(2) electroweak

S2×I2×T1

H7S2×I2×T1, Lem

photon U(1) electromagnetic

S2×I2×ℝ3×T1

H8S2×I2×ℝ3×T1

W±

bosons SU(2) electroweak

S2×I2×ℝ3×T1

H9I2, Lq

quintessence U(1)gravitation −

vacuum field

H10 I2×ℝ3, Ls

gluons SU(3) strong