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SAROD-2005 1 PHYSICAL PRINCIPLES FOR PROPULSION SYSTEMS
01.05.2014 20:07
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= 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=−∇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
∇× 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 vP I−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 /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*−qP−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, xl0 , and
right, xr0 , boundaries of the spatial integration
interval that is, x lsl t f and xrsr 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 nxBnK BxK−B* Bx
*
S K−q* ¿
v K
* =v K
S K−qK
S K−q* +
P*−PK n yBnK ByK−B* By
*
S K−q*
EK
* =EK
S K−q K
S K−q* +
P* q*−PK q KBnK 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
m2
−4 a2 c A
2 . (14)
FHLLC={ Fl if 0sl
Fl
* =Flsl Ul
* −Ul if sl≤0≤q*
Fr=Frsr Ur
* −Ur * if q*≤0≤sr
Fr if sr0 }.
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
=∇×⇒{∂ bx
∂ t
=∇yz
∂ b y
∂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 =12
[bx ,i1/2, j bx ,i−1/2, j ]
By i , j=12
[b y ,i , j1/2b 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 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 , 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 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 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 mi from ℝ4H8ℝ4 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 c2
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 ; tn= 1
n3t 1
v n =n v 1 ; cn =n c1
G n=1
n
G; 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
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 =1.3107 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.hpccs
pace.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 +
S 2×I 2 H5S2×I 2 , Lgp − neutral
three types of
gravitophotons
U(1)´ U(1) gravitation + -
vacuum field
S 2×I 2×ℝ3 H6S2×I 2×ℝ3 , Lew Z0 boson SU(2) electroweak
S 2×I 2×T1 H7S2×I 2×T 1 , Lem
photon U(1) electromagnetic
S2×I 2×ℝ3×T 1 H8S2×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
Heim's Theory of Elementary Particle Structures
01.05.2014 19:54
Journal of Scientific Exploration. Vol. 6, No. 3, pp. 217-231, 1992 0892-33 10192
O 1992 Society for Scientific Exploration
Heim's Theory of Elementary Particle Structures
T. AUERBACH
CH-5412 GebenstorJ Switzerland
ILLOBRANVDON LUDWIGER
Messerschmitt-Biilkow-Blohm, 0-8012 Ottubrunn, Germany
Abstract-Heim's theory is defined in a 6-dimensional world, in 2 dimensions
of which events take place that organize processes in the 3 dimensions of our
experience. A very small natural constant, called a "metron", is derived, representing
the smallest area that can exist in nature. This leads to the conclusion
that space must be composed of a 6-dimensional geometric lattice of very small
cells bounded on all sides by metrons. The existence of metrons requires our
usual infinitesimal calculus to be replaced by one of finite areas.
The unperturbed lattice represents empty vacuum. Local deformations of the
lattice indicate the presence of something other than empty space. If the deformation
is of the right form and complexity it acquires the property of mass and
inertia. Elementary particles are complex dynamical systems of locally confined
interacting lattice distortions. Thus, the theory geometricizes the world by
viewing it as a huge assemblage of very small geometric deformations of a 6-
dimensional lattice in vacuum. The theory also has significant consequences for
cosmology.
Introduction
The present article provides an overview of Burkhard Heim's unified field theory
of elementary particles and their internal structures (Heim, 1989, 1984; v.
Ludwiger, 1979, 1981, 1983). Various old and new concepts enter into the theory,
including cosmology, quantum field theory, organizing processes similar to
Sheldrake's morphogenetic fields (Sheldrake, 1985), and the existence of a
smallest area in a 6-dimensional world. The main results of Heim's theory are
formulas for the masses of elementary particles. Results turn out to be in very
good agreement with measured values.
This report is written with the aim of describing the basic architecture of
Heim's theory in mainly non-technical terms for the benefit of the average JSE
reader with a scientific background, who is not necessarily a physicist. For this
reason the terminology of field theory is often replaced by less specific but more
readily comprehensible expressions. In an Appendix selected topics are discussed
in more technical terms for the benefit of physicists.
The 6-Dimensionality of the World
It is well known in physics that energy is stored in the gravitational field surrounding
any material object. Heim concludes that in accordance with Einstein's
relation E = mc2 (E = energy, m = mass, c = velocity of light = 300'000 krnls) this
218 T. Auerbach and I. von Ludwiger
field energy must have associated with it a field mass, whose gravitation modifies
the total gravitational attraction of an object. In addition, the field mass gives
rise to a second gravitational field. The relation between the two fields is very
similar to the relation between electric and magnetic fields (Auerbach, in press).
The result of this is a set of equations governing the two dissimilar gravitational
fields quite analogous to those describing the electromagnetic fields
(Maxwell's equations). The main difference is the appearance of the field mass
in the gravitational equations in the place where zero appears in Maxwell's equations.
The zero in the latter is due to the non-existence of magnetic monopoles.
This difference renders Heim's gravitational equations less symmetric than
the electromagnetic ones. The same lack of symmetry also applies to a unified
field theory, combining electromagnetism and gravitation, which cannot be more
symmetric than its parts.
In the macroscopic world the general theory of relativity has introduced a new
concept into physics. It assumes that the properties of space itself are modified
in the presence of masses. The equations of relativity are restricted in the sense
that they only govern gravitation. In addition, they are too symmetric to satisfy
the above asymmetry criterion and they cannot be extended to the microscopic
world of quantum theory. For this reason Heim regards relativity as an incomplete
description of nature. He does, however, accept its basic philosophy of
space being capable of deformation. How this can be visualized will be discussed
in Section 5.
On passing from the macrocosm to the microcosm of elementary particles
Heim relates quantities describing the deformation of space to the energy states
of the system responsible for the deformation, in analogy to general relativity.
Energy states are known to occur in discrete, so-called "quantum" steps, like the
discrete energy levels of hydrogen atoms. These considerations determine the
general form of equation describing the microscopic states of a system in Heim's
theory.
Einstein's general relativity results in a set of 16 coupled equations (6 of
which occur twice). The figure 16 is equal to the square of the number of dimensions.
Hence, according to relativity, our world appears to be 4-dimensional
(because 16 = 4*) and consists of 3 real dimensions and one dimension proportional
to time.
In contrast, Heim finds 36 equations describing the microcosm. Again, this
must equal the square of the number of dimensions, so that the microscopic
world appears to be at least 6-dimensional. Since there can only be one set of
laws in nature it must be possible by appropriate transformations to carry the
microscopic equations over into the macroscopic world and vice versa. The conclusion,
therefore, is that the universe we live in is at least 6-dimensional and not
4-dimensional.
The 5th and 6th Dimensions
It can be shown that the number of real dimensions, i.e. those measurable with
yardsticks, is limited to 3. All higher dimensions must be of a different nature
Elementary particle theory 219
entirely. The 4th dimension, for example, is proportional to time, which is measured
with clocks and not yardsticks. The 5th and 6th dimensions will have to be
something different again (Cole, 1980), and according to Heim they are associated
with organizational properties. They will be called "transdimensions" or
"transcoordinates" to distinguish them from the four dimensions with which we
are all familiar.
Modern superstring theory describing the interactions between elementary
particles also involves the use of more than 4 dimensions. However, following a
suggestion by the mathematicians Kaluza and Klein, all but 4 of them curl up in
such a manner that they exist only in dimensions of the order of m. Thus
they are hidden and do not manifest themselves in the macroscopic world.
There exists an analogy between Sheldrake's theory of morphogenetic fields
and Heim's organizational 5th and 6th dimensions. Consider the following illustrative
example: A house is a highly organized structure. Before it can be built,
however, an architect has to draw up a construction plan. This plan is necessary,
but not sufficient. Workmen and building material must be available, too, and all
three in time combine to raise the structure whose details correspond to the original
design. The house, when finished, exists in the usual 3-dimensional space
and is connected only indirectly to the architect's plan and to the workers.
Events taking place in the 5th and 6th dimensions mirror the activities just
described. The processes unfolding in the two transdimensions establish an organizational
scheme for a certain structure and cause it to become reality. Both
dimensions always act together, no event of any kind can involve only one of
them. In fact, every event must involve both dimensions. Most structures being
organized exist in the 3-dimensional world of our experience (4 if time is included),
but extend into the two transdimensions.
Heim's theory is mathematical, but the organization of highly complex structures
such as houses or living cells cannot be described by mathematics alone.
Elementary particles, on the other hand, are organized structures, too, involving
the two transdimensions, yet their complexity stays within limits and allows
them to be treated mathematically.
Maximum and Minimum Distance. The Metron
The existence of a field mass, mentioned in Section 1, leads to a modification
of Newton's law of gravitation. Newton's law is simple and specifies the force
between two masses in terms of the distance separating them. As is well known,
the force is inversely proportional to the square of the distance.
Due to the existence of field mass the gravitational force in Heim's theory is
the solution of a so-called "transcendental" equation, i.e. an algebraic equation
having no simple solution. Nevertheless, approximate analytical solutions, i.e.
formulas, can be found for various ranges of the distance between two masses.
Purely numerical answers on a computer can, of course, be obtained for all distances.
As is to be expected, Heim's law is virtually indistinguishable from Newton's
law out to distances of many light years (1 light year = 5.91 trillion (1012) miles).
220 T. Auerbach and I. von Ludwiger
Thereafter, the force begins to weaken more rapidly than Newton's law and goes
to zero at an approximate distance of 150 million light years. At still greater distances
it becomes weakly repulsive. Finally, at a very great maximum distance it
goes to zero and stays zero. This distance is significant for the size of the universe,
because at distances exceeding it the force becomes unphysical. Hence,
greater distances cannot exist. The greatest possible distance in 3 dimensions is
the diameter of the universe, which will be denoted by the letter D.
A similar deviation from Newton's law also occurs at very small distances,
and there exists a very small minimum distance beyond which the force again
becomes unphysical. This distance turns out to be just about 4 times smaller than
the so-called Schwarzschild radius of general relativity, which is closely related
to the formation of black holes.
Even more significant than the maximum and minimum distances is a third
distance relation derived from Heim's gravitational law. In the limit of vanishing
mass, i.e. in empty space, a non-vanishing relation can be derived, involving the
product of the minimum distance and another small length, known in quantum
theory as the Compton wavelength of a given mass. This product of two lengths
clearly is an area, measured in square meters (m2). The product exists even when
the mass goes to zero and turns out to be composed of natural constants only. It,
therefore, is itself a constant of nature. Heim calls it a "metron" and designates it
by the symbol T (tau). Its present magnitude is
The significance of a metron is the fact that it exists in empty, 6-dimensional
space. The conclusion is that space apparently is subdivided into a 6-dimensiona1
lattice of metron-sized areas. This is a radical departure from the generally
held view that space is divisible into infinitely small cells. Independently of
Heim, other authors in an attempt to quantize gravitation have found elementary
areas of dimensions similar to that of a metron (Ashtekar et al., 1989).
Metronic Mathematics
The result that no area in Heim's 6-dimensional universe may be smaller than
a metron requires a revision of some branches of mathematics. For example, differentiation
assumes that a curve or line can be decomposed into an infinite
number of infinitely small segments. Conversely, integration recomposes the
infinitely small segments back into a curve of finite length.
In Heim's theory differentiation and integration must be changed to comply
with the metronic requirements mentioned above. A line cannot be subdivided
into infinitely small segments, because an infinitesimal length cannot be part of
an area of finite, metronic size. Similarly, integration is changed into a summation
of finite lengths. While the mathematics of finite lengths has been developed
in the literature (Norlund, 1924; Gelfond, 1958) the novel feature of
Heim's metronic theory is that it is a mathematics of finite areas.
Elementary particle theory 22 1
Obviously, the metronic area of lop7' m2 is exceedingly small. The surface
area of a proton, for example, is much greater, i.e. about 3 x m2. A metron
is so tiny that for many applications it may be regarded as infinitesimal in the
mathematical sense. In such cases Heim's metronic mathematics goes over into
regular mathematics. There are instances, however, when it becomes obligatory
to use metronic differentiation and integration.
The Building Material of Elementary Structures
Empty space has been shown to consist of an invisible lattice of metronic
cells. One can visualize them as little (6-dimensional) volumes, whose walls are
metrons, touching each other and filling all of space. The orientation of the walls
in space is important, because Heim shows that it is related to the quantum
mechanical concept of spin, but this feature will not be further discussed in the
present report.
Uniformity of the lattice signifies emptiness. Conversely, if the lattice is locally
deformed or distorted, this deformation signifies the presence of something
other than emptiness. If the deformation is complicated enough, it might, for
example, indicate the presence of matter. This implies that there really is no separate
substance of which particles are composed. What we term "matter" is nothing
but a locally confined geometric structure in vacuum. Pure vacuum has the
ability of deforming its 6-dimensional lattice structure into geometrical shapes.
That portion of it, which extends into the 3-dimensional space of our experience
is interpreted by us as matter.
The situation is somewhat analogous to the formation of a vortex in air. Still
air corresponds to complete emptiness having no recognizable geometric properties.
A tornado, on the other hand, is a fairly well defined geometric structure in
air. Its funnel-like shape clearly differentiates it from the surrounding atmosphere,
which is not in rotation, but it still consists of air only and not of any separate
material.
The same is true of geometrical structures in vacuum. They clearly differ from
complete emptiness, but their "construction material" nevertheless is vacuum. It
should be emphasized, however, that a mere deviation from uniformity of the
metronic lattice does not automatically constitute matter.
Metronic Condensations
The term metronic "condensation" is frequently used by Heim in connection
with the structure of elementary particles. Since the concept cannot be visualized
in 6 dimensions it will be explained with the aid of a 3-dimensional model.
Figure 1 illustrates a transparent sheet with a central bulge. The sheet is covered
with a square lattice of straight lines. Each of the many squares formed in
this manner is supposed to represent a metron, so that the whole may be called a
"metronic sheet". Note that the metrons are not distorted, although the sheet is.
Also drawn are 3 rectangular coordinate axes denoted by x, y, and z. They may
T. Auerbach and I. von Ludwiger
Light 1
Fig. 1. Metronic condensations in 3 dimensions.
be thought of as marking three comers of a room whose floor is the x-y-plane,
and whose 2 vertical walls are the x-z- and y-z-planes.
If the sheet is illuminated from above and from the right the grid lines on the
sheet will cast shadows on the floor and on the left wall, as shown in the drawing.
In technical language these shadows are called projections of the grid on the
Elementary particle theory
Earth
Fig. 2. Distortion of space and its metronic condensation caused by the earth-moon system.
respective walls. It is immediately evident that the square metrons in certain
regions of the projected images become narrow rectangles. These regions are the
metronic condensations referred to in the heading, because the squares are compressed,
or condensed, in one direction. There exist areas of maximum condensation,
where the projected metrons are compressed into thin lines, and other
areas, where they project essentially as uncompressed squares. Note that some
areas on the metronic sheet showing minimum condensation in the x-z-plane
show maximum condensation in the x-y-plane. The importance of condensations
lies in the fact that for some applications it is easier to describe the properties of
a structure by referring to its projections on vertical walls rather than by considering
its full description in 3 or more dimensions.
224 T. Auerbach and I. von Ludwiger
According to general relativity a material object distorts space. This is illustrated
in Fig. 2 for the earth-moon system. Space is pictured as a kind of rubber
sheet into which the heavy earth and the much lighter moon sink in to different
depths. In Heim's theory the sheet is covered with a net of metronic squares.
This enables one to express the space curvature, as the distortion is called in
general relativity, by examining the density of compressed metrons in the projection
of the sheet on a 2-dimensional plane, as shown in Fig. 2.
It should be emphasized that Figs. 1 and 2 even in 3 dimensions are convenient
simplifications of the true situation. The unperturbed metronic lattice, as
mentioned in Section 5, is a network of cubes. A disturbance would create a distorted
volume which might be pictured as a sequence of distorted parallel sheets,
the most deformed of which are pictured in the two drawings. The distortion
diminishes with increasing distance of the sheets from the one drawn, until the
undisturbed cubic lattice is reestablished .
The deformation need not be static. It can rotate or pulsate or change shape in
some other dynamical way, and the projections will follow suit.
This picture can now be generalized to a 6-dimensional lattice with a localized
static or dynamic deformation, forming a condensation, i.e. projecting a
3-dimensional pattern into our world. The 3-dimensional projections in 6-space
are the generalizations of the 2-dimensional projections in 3-space illustrated in
Figs. 1 and 2. Such condensations form the basis of matter and elementary particles.
A piece of matter that can be seen and touched is merely the projection into
our 3-dimensional space of the true, 6-dimensional lattice deformation, just as
the shadow of a tree is the 2-dimensional projection of its true 3-dimensional
structure.
The 4 Types of Elementary Structures
The uniform metronic lattice characterizing empty space can be distorted in
several fundamental ways, most of which involve fewer than 6 coordinates. This
may be visualized by noting that the two projected areas in Fig. 1 are each compressed
in one direction only. In this simple example one dimension is distorted,
the other is not. A space consisting of fewer than 6 dimensions is called a "subspace".
The statement at the end of Section 6 can now be reworded in the sense
that what we regard as matter is nothing but a locally confined condensation in
our 3-dimensional subspace due to a local deformation of the 6-dimensional
metronic lattice. Heim finds that there exist 4 basic types of deformation in
6-space, which are discussed below.
a) The first type is a lattice deformation involving only the 5th and 6th coordinates.
In the 4 remaining dimensions the metronic lattice remains undisturbed.
Physically, this may be interpreted as a structure existing in the
two transdimensions. Since our senses are not attuned to events in the two
transdimensions this may be difficult to visualize.
Although the deformation exists in dimensions 5 and 6 only, and does
not project directly into our 3 dimensions, its effect may occasionally be
Elementary particle theory 225
felt in the rest of the world. Under certain conditions it may extend into
the four remaining dimensions in the form of quantized gravitational
waves, so-called gravitons. The equations show that gravitons should
propagate with 413 the speed of light. Thus, according to Heim gravitational
waves have a speed of 400'000 krnhecond.
The situation is somewhat analogous to a strong vortex like a tornado
confined to a relatively narrow region in air, nevertheless sending sound
waves out to very great distances, where the air is not yet affected by the
vortex motion. Summarizing, the first type of deformation may be viewed
as a structure in the 2 transdimensions capable of emitting gravitational
waves that we should be able to register.
b) The second type of deformation again involves dimensions 5 and 6, and in
addition time, the 4th dimension. Again, this particle-like structure does
not project directly into our 3-dimensional world, but is felt here only in
the form of waves. Heim derives the property of these waves and shows
that they are identical to those of electromagnetic light waves or photons.
It follows that case (b) describes a particle-like structure in the 4th, 5th,
and 6th dimensions, extending into the remaining 3 dimensions in the
form of photons.
c) The third possible deformation involves 5 dimensions, i.e. all coordinates
except time. This 5-dimensional structure projects into the 3-dimensional
space of our experience, i.e. it forms a condensation here, and it is reasonable
to assume that we are sensitive to such condensations. This is indeed
the case, and Heim shows that they give rise to uncharged particles with
gravitational mass and inertia.
d) The final deformation involves all 6 coordinates. This again leads to
3-dimensional condensations, giving rise to particles, but, as in case (b),
the inclusion of time leads to electric phenomena as well. Heim can show
that 6-dimensional lattice distortions lead to charged particles.
Cosmology
In Heim's theory both the metronic size z and the largest diameter D depend
on the age of the universe. The dependence is such that D is expanding and z is
contracting, so that D was smaller in the past and z was larger. It stands to reason
that at one time in the distant past the surface area of a sphere of diameter D
in our 3-dimensional world was equal to the size of z. This instant marks the origin
of the universe and of time.
The mathematical relation between D and z is not simple, so that 3 different
values of D are found to satisfy the criterion that the area of a sphere of diameter
D be equal to z at the beginning of time. Evidently, the universe started as a trinity
of spheres, whose diameters turn out to be (in meters):
226 T. Auerbach and I. von Ludwiger
This trinity of spheres has important bearings on the structure of elementary
particles.
From the first moment on the universe began to expand, though at a slower
rate than is presently predicted on the basis of the red shift of distant galaxies
(see the Appendix). Heim's theory results in a present age of the universe
approximately equal to 5.45 x 10'07 years, and a diameter D of about 6.37 x
101°9 light years. During most of its existence the universe consisted of an empty
metronic lattice, whose metrons kept getting smaller as the universe grew larger.
Eventually, metrons became small enough for matter to come into existence.
This may have occurred some 15-40 billion (lo9) years ago, at which time matter
was created throughout the volume of the universe. Hence, according to
Heim matter did not originate very soon after a "big bang" explosion but more
uniformly in scattered "fire-cracker" like bursts, perhaps of galactic proportions.
Spontaneous uniform creation of matter, coupled with the partly attractive and
partly repulsive force of gravity mentioned in Section 3 resulted in the observed
large-scale galactic structure of the universe. Creation of matter continues to this
day, though on a very much reduced scale.
The Structure and Masses of Elementary Particles
More than three quarters of Heim7s second volume are devoted to the derivation
of his final formula for the masses of elementary particles in the ground
state and in all excited states. Only the barest outline of the structural complexity
of elementary particles can be presented here.
The interior of an elementary particle must be viewed as consisting of a number
of metronic condensations in various subspaces. The configuration which is
projected into our 3-dimensional physical world consists of 4 concentric zones
occupied by structural elements. Maxima and minima of these condensations in
the sense of Figs. I and 2 participate in a rapid sequence of periodic, cyclic
exchanges. The internal structures undergo continuous modifications during this
process until, after a certain short period of time, the original configuration is
reestablished. This period is the shortest lifetime a particle possessing mass and
inertia can have. In general, a lifetime consists of several such periods. If the initial
configuration is not regained after the last period the particle decays. A particle
is stable only if its structure always returns to its original form. The subdivision
into 4 zones is a consequence of the original trinity of spheres
characterizing the universe during the first instant of its existence.
The actual mass and inertia are not a property of the 3-dimensional structures
themselves, as might be thought. Instead, they are the secondary result of
exchange processes between the 4 internal zones described above. These
processes are the actual carriers of mass and inertia. For this reason, Heim's elementary
particles definitely are not composed of subconstituents such as quarks.
The inner 3 structural zones are difficult to penetrate, the innermost being almost
impenetrable. In scattering experiments they might create the illusion of 3 partiElementary
particle theory 227
cles being present in the interior. Empirical predictions that have led to the formation
of quark theory can be interpreted by Heim in geometrical terms.
All states of an elementary particle are characterized by 4 genuine quantum
numbers. The first 3 are the baryonic number k (k = 1 or 2), the isotopic spin P,
and the spin Q. The fourth number can only be either 0 or 1. In addition, there is
a number +1 or -1 characterizing particle or antiparticle, a number indicating
whether a particle is charged or not, and a number N = 1, 2, . . . specifying the
state of excitation. 4 more quantum numbers refer to the 4 structural zones.
These, however, cannot be chosen at will but are derived from the numbers listed
above.
Results for the ground states are in excellent agreement with experiment. In
addition to the known particles, Heim predicts the existence of a stable neutral
electron and its antiparticle, with masses about 1% smaller than the masses of
their charged counterparts. Furthermore, Heim predicts 5 neutrinos with masses
ranging from 0.00381 eV to 207 keV (1 electron Volt is the mass equivalent of
1.7826 X kg, 1 keV = 1000 eV). On the other hand, the number of excited
states each particle can have turns out to be much too large. So far Heim has not
succeeded in finding a criterion which would limit the number of excited states
to those actually observed.
Summary and Outlook
The essence of Heim's theory is its complete geometrization of physics. By
this is meant the fact that the universe is pictured as consisting of innumerable
small, locally confined geometric deformations of an otherwise unperturbed
6-dimensional metronic lattice. The influence these deformations have on our
4-dimensional world, or the effects of their projections into it, constitute the
structures we interpret as gravitons and photons, as well as charged and
uncharged particles. The theory ultimately results in a formula from which the
masses of all known elementary particles and a few unknown ones may be
derived. In addition, it provides a picture of cosmology differing widely from
the established one.
Despite the insight gained into particle physics, the theory is not entirely
equivalent to modem quantum theory. For this reason Heim has extended the
theory to 12 dimensions. Only this extension allows full quantization, and as a
consequence it becomes possible to unite relativity and quantum theory. Even 6
dimensions are not sufficient to accomplish this. A more detailed account of
these new developments will be published in a 3rd volume (Heim, personal
communication).
While the organization of elementary particles still lends itself to mathematical
treatment, higher structures, in particular living beings, are far too complex
to be dealt with in this manner. Nevertheless, Heim has extended his theory to
that territory as well by using the method of mathematical logic. This enables
him to derive logically precise statements about the process of life, the origin of
paranormal phenomena, and the structure of realms far transcending the
228 T. Auerbach and I. von Ludwiger
4-dimensional world of our experience (Heim, 1980, v. Ludwiger, 1979). This
extension of the mathematical theory may, in fact, be regarded as Heim's most
important contribution to the understanding of nature. Unfortunately, only nonmathematical
summaries of the theory have been published so far. A fully mathematical
formulation exists only in the form of an unpublished manuscript.
Appendix
In this appendix a few selected topics are summarized in more technical detail.
The Field Equations
In analogy to Einstein's attempt in 1946 to develop a unified field theory
Heim works with non-symmetic, complex (i.e. non-Hermetian) metric tensors.
Einstein used a single metric tensor, g,, where
The symmetric part of Eq. (1 ), gik, was interpreted as gravitational potential,
and the antisymmetric part, gik, as electromagnetic potential. In contrast to this,
Heim generates a basic metric tensor, x,, in a 6-dimensional hyperspace by coupling
together 3 interacting matrices, g!k), g!:), and gl;), in the form of
The three gi,'s arise from the combination of various subspaces.
All operations require the use of metronic mathematics, so that differential
equations and tensor equations are replaced by their metronic equivalents. The
metronic size is
(y = gravitational constant, h = Planck's constant).
The field equations in Heim's theory are eigenvalue equations of the general
form
where 0 is a metronic operator, h is an eigenvalue, and y/ is an eigenfunction. h
and y/ characterize all permissible geometric configurations of the 6-dimensional
metronic lattice.
In Einstein's field equations of gravitation the curvature tensor R, in a
4-dimensional space geometry is proportional to the energy-momentum density
Elementary particle theory 229
tensor T,. For this reason space curvature in general relativity can exist only in
the presence of energy and matter.
In contrast, Heim's operator 0, Eq. (3), involves only terms consisting of
purely geometric metronic partial derivatives and generates the structure states y
in Eq. (3). Matter and energy are generated by dynamic processes involving the
metrons. The spectrum of all possible masses derived from Eq. (3) corresponding
to the uncharged and charged particles mentioned under (c) and (d), Section
7, is nearly continuous. Most of Vol. 2 of Heim's books therefore is devoted to
separating out the discrete spectrum of observed elementary particles from the
nearly continuous background.
The Red Shift
As mentioned in Section 3, matter exerts a weakly repulsive force over very
great distances. Repulsion reduces the energy of light rays passing through these
regions and results in a shift of the spectrum towards the red. According to
Heim, this accounts for the entire observed red shift, the contribution of the
expanding diameter D of the universe being insignificant. His calculation of the
Hubble radius is in good agreement with observation if use is made of the somewhat
uncertain density of matter in the universe.
The Entropy Problem
Matter seems to be a relatively late by-product of a universe which remained
empty for a very long period of time, except for the existence of geometric
quanta in the form of metrons. For this reason the entropy problem arising in
connection with the big-bang model is avoided.
This problem refers to the fact that, since entropy is known to increase with
time, in the past it must have been much smaller than it is now. Conversely, the
thermal order of the universe must have been greater. Calculations (Penrose,
1989) show that the degree of order in a near point-like universe shortly after the
big bang must have been about 101O"'timesg reater than now to produce the order
existing today. This is avoided in Heim's theory, which postulates that matter
came into existence only after the diameter of the universe already had reached a
very large size.
The ERP-Paradox
The Einsteln-Rosen-Podolsky (ERP) paradox of quantum theory (Einstein et
al., 1935), has remained unresolved since its inception in 1935. Einstein and
Bohm developed hypotheses of "hidden variables", i.e. processes on a subnuclear
scale. These are not accessible to direct observation and for this reason
appear to us as the uncertainties of quantum theory, although in reality they are
determinate processes.
The hidden variable theory has not generally been accepted by physicists.
Penrose (Penrose, 1989) surmises that only a quantized general relativity will
230 T. Auerbach and I. von Ludwiger
properly resolve the wave-particle duality at the bottom of the ERP paradox. It
should also explain the multitude of elementary particles and eliminate the
infinities of quantum field theory.
Heim's theory fulfills these requirements. It explains the origin of particles
and is devoid of infinities because its mathematics utilizes the finite size of
metrons. Its "hidden variables'' are organizational states resulting in a world that
is neither wholly predictable nor wholly unpredictable.
The Fine Structure Constant
Dirac at one time pointed out that the right unified field theory may be identified
by the fact that it correctly reproduces Sommerfeld's fine structure constant
a - 11137. Heisenberg felt that he was on the right track when his spinor theory
led to a value of 11120. The reader may check for himself that Heim's constant
comes closer by several orders of magnitude to the measured (1987) value of
a = 1/137.035989(5).
a turns out to be the solution of a fourth order equation, involving only a2 and
a4. Its solution is
The numerical values of the fine structure constants are
a- = 11137.0360085
a+ = 111.000026627.
Outlook
An in-depth analysis of the trinity of spheres existing at time t = 0 reveals the
possibility of deriving from set theory all well-known coupling constants plus a
Elementary particle theory 23 1
few additional ones. Work on this problem is currently in progress (Heim,
Droscher, private communication).
References
Ashtekar, A,, Smolin L., Rovelli, C., & Samuel, J. (1989). Quantum Gravity as a Toy Model for the 3+1
Theory. Classical Quantum Gravity 6, (10) L 185-L 193.
Auerbach, T. The Generation of Antigravity. To be published in MUFON-CES Report No.. 11, I . v. Ludwiger
editor, Feldkirchen-Westerham, Germany.
Cole, E.A.B. (1980). I1 Nuovo Cimento 55B, 269-275.
Einstein, A., Rosen N., and Podolsky, B. P. (1935). Phys. Rev. 47, 777.
Gelfond, A.O. (1958). Differenzenrechnung. Hochschulbucher fur Mathematik, Vol. 41, Berlin, VEB
Deutscher Verlag der Wissenschaften.
Heim, B. (1989 (revised)). Elementarstrukturen der Materie, Val. I. Resch Verlag, Innsbruck, Austria.
Heim, B. (1984). Elementarstrukturen der Materie, Vol. 2. Resch Verlag, Innsbruck, Austria.
v. Ludwiger, I. (1979). Die einheitliche 6-dimensionale Quanten-Geometrodynamik nach Burkhard Heim,
in: Ungewohnliche Eigenschaften nichtidentGzierbarer Lichterscheinungen, 267-331, MUFON-CES,
Feldkirchen-Westerham .
v. Ludwiger, I. (1981). in: Heimsche einheitliche Quantenfeldtheorie, Resch Verlag, Innsbruck, Austria.
v. Ludwiger, I. (1983). Die innere Struktur elementarer Subkonstituenten der Materie, in: Seltsame Flugobjekte
und die Einheit der Physik, 271403, MUFON-CES, Feldkirchen-Westerham.
Norlund, N.E. (1924). Vorlesungen iiber Differenzenrechnung, Springer Verlag, Berlin.
Penrose, R.T. (1989). The Emperor's New Mind-Concerning Computers, Minds, and the Laws of Physics,
Oxford University Press.
Sheldrake, R. (1985). A New Science of Life, Anthony Bond, London.
Raumfahrt- Was ist das?
01.05.2014 19:45
Raumfahrt- Was ist das?
Internationale Junior Universität Salzgitter
20. April 2005
Dr. rer. nat. Jochem Häuser, Professor
Univ. of Applied Sciences
Fakultät Karl-Scharfenberg, Salzgitter
www.hpcc-space.de, jh@hpcc-space.de
Acknowledgments
This research was partly funded by the ministry of Science and
Culture of the State of Lower Saxony, Germany and the
European Commission under contract EXTV 1999.262.
Dipl.-Ing. T. Gollnick and Dipl.-Ing. O. Rybatzki, Univ. of
Applied Sciences, Salzgitter helped in the preparation of this
talk.
Vorlesung Überblick
Unser Standort
Raumfahrtpioniere
Gefahren in der Raumfahrt
Wie kommt man in denWeltraum
Das Antriebssystem
Trajektorie (Flugbahn)
Aerodynamische Stabilität
Hitzeschutzschild
Computer Simulation
Diskussion und Ausblick, neue Antriebe
Raumfahrtpioniere
Wie kommt man in den
Weltraum
Das Antriebssystem
Gefahren in der Raumfahrt
The Columbia STS-107 mission lifted off on January 16,
2003, for a 17-day science mission featuring numerous
microgravity experiments. Upon reentering the atmosphere
on February 1, 2003, the Columbia orbiter suffered a
catastrophic failure due to a breach that occurred during
launch when falling foam from the External Tank struck
the Reinforced Carbon Carbon panels on the underside of
the left wing. The orbiter and its seven crewmembers (Rick
D. Husband, William C. McCool, David Brown, Laurel
Blair, Salton Clark, Michael P. Anderson, Ilan Ramon, and
Kalpana Chawla) were lost approximately 15 minutes
before Columbia was scheduled to touch down at Kennedy
Space Center. This site presents information about the STS-
107 flight, as well as information related to the accident and
subsequent investigation by the formal Columbia Accident
Investigation Board.
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Every solver object contains the data of and the numerics for one
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Trajektorie (Flugbahn)
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Objekt: 40 - 42 av 85
