SAROD-2005 1 PHYSICAL PRINCIPLES FOR PROPULSION SYSTEMS
20/05/2014 16:26
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 threedimensional
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 (nonrelativistic)
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. Twodimensional
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=¤ ¤e¤v×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 ∇פ∇×B¤=−∇2 B , 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
∇פ v×B¤ convection term and the ¤m∇2 B
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 v¤P I−B B
¤E¤P¤v−B¤v⋅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/¤¤−1¤¤¤¤u2¤v2¤w2¤/2
+¤Bx
2¤By
2¤Bz
2¤/2¤m
(4)
P=p¤¤Bx
2¤By
2¤Bz
2 ¤/2 ¤m. (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 spatiotemporal
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±c A ,u±cs ,u±c f ]. 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 to t f . A major task is the
evaluation of the wave propagation speeds.
q*=sM=
¤r qr ¤ sr−qr ¤−¤l ql ¤sl−ql ¤¤pl−pr−Bnl
2 ¤Bnr
2
¤r ¤ sr−qr ¤−¤l ¤sl−ql ¤
(6)
P*=¤¤sl−q ¤¤q*−q¤¤P−Bn
2 ¤¤Bn
* ¤2 . (7)
In order to evaluate the integrals, the (yet unknown)
signal speeds sl and sr are considered, denoting the
fastest wave propagation in the negative and positive xdirections.
It is assumed, however, that at the final time
t f , no information has reached the left, xl¤0 , and
right, xr¤0 , boundaries of the spatial integration
interval that is, x l¤sl t f and xr¤sr t f . 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
S K−q K
S K−q*
¤¤u ¤K
* =¤¤u ¤K
S K−qK
S K−q* +
¤P*−PK ¤ nx¤BnK BxK−B* Bx
*
S K−q* ¿
¤¤v ¤K
* =¤¤v ¤K
S K−qK
S K−q* +
¤ P*−PK ¤n y¤BnK ByK−B* By
*
S K−q*
EK
* =EK
S K−q K
S K−q* +
P* q*−PK q K¤BnK ¤B⋅v ¤K−B* ¤B⋅v ¤*
S K−q*
(8)
(9)
Byl
* =Byr
* =B y
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 =a2¤ B2
¤¤m
±¤¤a2¤ B2
¤ ¤m¤2
−4 a2 c A
2 . (14)
FHLLC={ Fl if 0¤sl
Fl
* =Fl¤sl ¤Ul
* −Ul¤ if sl≤0≤q*
Fr=Fr¤sr ¤Ur
* −Ur ¤* if q*≤0≤sr
Fr if sr¤0 }.
Bxl
* =Bxr
* =Bx
HLL=
sr Bxr−sl Bxl
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
=∇פ⇒{∂ bx
∂ t
=∇y¤z
∂ b y
∂t
=∇x¤z} (15)
¤ bx ,¤i¤1/2 , j¤=
¤t
¤ y
[¤z ,¤i¤1/2, j¤1/2¤−¤z ,¤i¤1/2, j−1/2¤]
¤ by ,¤i , j¤1/2¤=
-
¤t
¤ y
[¤z ,¤i¤1/2, j¤1/2¤−¤z ,¤i−1/2, j¤1/2¤]
(16)
∮b⋅dS=0⇒¤ y [bx ,¤i¤1/2, j¤−bx ,¤i−1/2, j¤]¤
¤ x[by ,¤i , j¤1/2¤−by ,¤i , j−1/2¤]=0
(17)
Bx¤i , j ¤=12
[bx ,¤i¤1/2, j ¤¤bx ,¤i−1/2, j ¤]
By ¤i , j¤=12
[b y ,¤i , j¤1/2¤¤b y ,¤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 x¤0
¤=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 , By ¤=¤−sin y , sin 2x¤
¤¤ , p , vz , 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 ℝ4¤H8¤ℝ4, has to replace the usual mapping
ℝ4¤ℝ4 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 polymetric
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 x m¤¤¤¤¤i ¤¤ from ℝ4¤H8¤ℝ4 resulting
in the metric tensor
g i 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.
g i k=: Σ
¤ , ¤=1
8
gi k
¤¤¤¤ (20)
g i 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:
g i k ¤ Hℓ ¤=: Σ
¤ , ¤∈H ℓ
g i 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=Awph . (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=vk vk
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 .
M H8 N
4 H8 4
l 1, . . . ,4
curvilinear
1, . . . ,8
Heim space Euclidean
m 1, . . . ,4
l xm
g ik
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 S2 I2 I2
gik
9
3
gik
10
T1
gik
11
3 T1
gik
g 12 ik
1
3
gik
2
T1
gik
3
3 T1
gik
4 gik
5
3
gik
6
T1
gik
7
3 T1
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
mp c¤2
d
d0
3 Z . (25)
d
[m]
D
[m]
I n
[An]
N wgpe ¤0 H
(T)
¤
0.2 2 6.6 ×106 1.4× 10-7 13 7×10-16
0.3 3 1.3 ×107 7.4 ×10-6 18 2×10-5
0.4 4 2.7 ×107 2×10-5 27 1.1×10-2
0.5 5 4 ×107 3.9×10-5 33 0.72
0.6 6 1.5 ×107 4.8×10-5 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
xi ¤ n¤= 1
n2 x ¤1 ¤ , i=1,2 ,3 ; t¤n¤= 1
n3t ¤1¤
v ¤n ¤=n v ¤1 ¤; c¤n ¤=n c¤1¤
G¤ n¤=1
n
G; ℏ¤n ¤=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
Br
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=
g gp
+
g g
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 =1.3¤107 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,
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[2] Krauss, L.M., “Propellantless Propulsion: The Most
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Breakthrough Propulsion Physics Workshop
Proceedings, NASA/CP-1999-208694, January
1999.
[3] Rovelli, C., “Loop Quantum Gravity”, Physics
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[4] Smolin, L., “Atoms of Space and Time”, Scientific
American, January 2004.
[5] Zwiebach, R., Introduction to String Theory,
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[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”,
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[9] Einstein, On the Generalized Theory of Gravitation,
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AIAA/ASME/SAE/ASE, Joint Propulsion
Conference & Exhibit, Ft. Lauderdale, FL, 7-10
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Table 2: The hermetry forms for the six fundamental physical interactions.
Subspace Hermetry form
Lagrange density
Messenger particle Symmetry
group
Physical
interaction
S2 H1¤S2¤ , LG
graviton U(1) gravity +
S 2×I 2 H5¤S2×I 2¤ , Lgp −¤ neutral¤
three types of
gravitophotons
U(1)´ U(1) gravitation + -
vacuum field
S 2×I 2×ℝ3 H6¤S2×I 2×ℝ3¤ , Lew Z0 boson SU(2) electroweak
S 2×I 2×T1 H7¤S2×I 2×T 1¤ , Lem
photon U(1) electromagnetic
S2×I 2×ℝ3×T 1 H8¤S2×I 2×ℝ3×T 1¤ W ± bosons SU(2) electroweak
S2×I 2×ℝ3×T 1 H9¤ I 2¤ , Lq
quintessence U(1) gravitation -
vacuum field
H10 ¤I 2×ℝ3¤ , Ls
gluons SU(3) strong
