AIAA 2005 - 4321 MAGNET EXPERIMENT TO MEASURING SPACE PROPULSION HEIM-LORENTZ FORCE
13/05/2014 18:39
AIAA 2005 - 4321
MAGNET EXPERIMENT TO MEASURING
SPACE PROPULSION HEIM-LORENTZ FORCE
Walter Dröscher1, Jochem Hauser 1,2
This paper describes in a non-mathematical way, by using a sequence of pictures, the physics of a novel space
propulsion technique and its experimental realization, based on a unified field theory in a quantized, 8-dimensional
space, developed by the late German physicist Burkhard Heim, termed Heim Quantum Theory (HQT or
HT). Following a strict geometrization principle introduced by the first author, HQT predicts six fundamental
interactions, requiring two additional gravitational like interactions, represented by gravitophotons (attractive
and repulsive, fifth interaction), and the quintessence or vacuum particle (repulsive, sixth interaction), enabling
a completely different type of propulsion, denoted gravitophoton field propulsion. The gravitophoton force,
would accelerate a material body without the need of propellant. Gravitophoton particles are generated in pairs
from the vacuum itself by the effect of vacuum polarization (virtual electrons), under the presence of a very
strong magnetic field (photons). Attractive gravitophotons interact with matter, and thus can become real particles,
exacting a force on a material body. In particular, the experimental setup is described to measure the so
called gravitational Heim-Lorentz force, which is a result of gravitophoton pair production. Experimental conditions
are discussed with emphasis to magnet design to obtaining the high magnetic field strengths to generate
an appreciable Heim-Lorentz force.
1Institut für Grenzgebiete der Wissenschaft (IGW), Leopold - Franzens Universität Innsbruck, Innsbruck, Austria
2 Faculty Karl-Scharfenberg, University of Applied Sciences, Salzgitter, Germany
1 Senior scientist, 2 Senior member AIAA, member SSE, Prof., www.hpcc-space.com or www.uibk.ac.at/c/cb/cb26/
ã 2005 Institut für Grenzgebiete der Wissenschaft, LEOPOLD - FRANZENS UNIVERSITÄT INNSBRUCK, AUSTRIA
41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Tucson, Arizona, 10-13 July, 2005
1 Field Propulsion Principles according
to Heim Theory2 3
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. Furthermore, the assumption of locality
for all physical interactions is of greatest importance and
determines the general structure of a unified theory as
well as the number of fundamental physical interactions.
Following this geometrization principle (Sec. 2) leads to a
poly-metric that describes all fundamental interactions,
but also predicts two additional gravitational like interactions
represented by massless particles named gravitophoton
(both attractive and repulsive), and a particle
termed quintessence or vacuum particle (repulsive) that is
identified with dark energy. Due to gravitophoton pair
production, the total energy extracted from the vacuum is
zero. In addition, the theory predicts the conversion of
photons into gravitophotons and, under special conditions
(very strong magnetic fields), the conversion into quintessence
particles. Since the coupling constants for these
two additional gravitational interactions can be calculated
in Heim's theory, quantitative predictions of the gravitophoton
interaction are possible. The equation describing
this force is termed the Heim-Lorentz equation, because
of its structural similarity with the magnetic Lorentz force
(mathematical details are given in [13, 14]). However, the
Heim-Lorentz force is a gravitational force, generated by
pair production of gravitophotons (attractive, graviton
like) and repulsive from the vacuum. No energy is extracted
from the vacuum, but the cross section of the
attractive (or negative, with regard to energy) gravitophoton
for interaction with matter is much larger
than for the repulsive (or positive) gravitophoton, so
2 The picture on the front cover depicts the six fundamental interactions
resulting from HQT. There should exist two additional gravitational
like forces that can be both attractive and repulsive. The gravitophoton
particles are generated from photons, and thus HQT predicts
an interaction between electromagnetism and gravitation. The
letter H with an index (indices 6 and 8 in the picture are not correct,
see Table 3) stands for hermetry form, a concept described in Sec.
2.1.
3 For nomenclature and glossary see www.hpcc-space.com under Publications:
HeimTheoryGlossary.pdf
that a net force on material objects is exerted once
gravitophoton pair production begins. In Secs. 3 and
4 a discussion of the experimental realization of the
Heim-Lorentz force is presented.
The theory also predicts an interaction of repulsive
gravitophotons with gravitons, for instance the gravitophotons
of the spacecraft, leading to a production
of quintessence particles, and consequently reducing
its gravitational potential F. This would require either
a reduction of the mass of the spacecraft or a reduction
of the magnitude of the gravitational constant
G. For a reduced mass, conservation of momentum
would require a velocity c' > c in ¤ 4. Both, Heim and recent
loop gravity theory do predict a quantized minimal
surface area which is
8
3
Gc
3 . The factor
8
3 cannot be determined directly from loop quantum
gravity, but was chosen to fit the Bekenstein-Hawking
formula for the entropy of a black hole [7, 9]. Heim
performed a phenomenological derivation and obtained
the factor ¾
. Any physical phenomenon requiring a
gravitational constant G' < G or a speed of light c' > c in
¤ 4 therefore has to be ruled out, violating the fact that
is
the minimum surface. On the other hand, because of positive
gravitophoton action,
is actually reduced. In order
to resolve this contradiction, it is postulated that the object
has to leave our spacetime and enters into a parallel
space (or parallel universe or multiverse), denoted as ¤ 4
(n) with n
. It seems to be possible that a spacecraft,
under certain conditions, stated below by Eq. 12, will be
able to enter into such a parallel space. Covariant physical
laws hold in parallel space ¤ 4(n) with respect to ¤ 4, but
the gravitational constant, the mass of the spacecraft, and
the speed of light are changed according to G(n)=G/n, M
(n)=nM, and c(n)= nc where n is larger than 1. In such a
space, superluminal speeds would be possible in principle.
The interesting fact is that an object can transit into
parallel space at a relatively low speed from our own
¤ spacetime 4, so no excessive energy input is needed.
2 Heim Quantum Field Theory and the
Physics of Elementary Particles
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 suc-
2
cessful in constructing a quantum theory of gravity. In
how far string theory [1, 3], 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. [4, 5, 7, 10, 12]. 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 [6]. 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 forming subspace
S2 (see glossary), and coordinates x7, x8 describing
information forming subspace I2, i.e., quantum mechanics,
resulting in an 8-dimensional discrete space in
which a smallest elemental surface, the so-called metron,
exists.
¤
comprises real fields, the hermetry
forms, producing real physical effects. One of these
hermetry forms, H12, is responsible for gravity, but there
are 11 other hermetry forms plus 3 degenerated hermetry
forms, part of them listed in Table 3. The physics in
HQT is therefore determined by the poly-metric of the
hermetry forms. This kind of poly-metric is currently
not included in quantum field theory, loop quantum
gravity, or string theory.
2.1 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. 1- 6. The
mathematical derivation for hermetry forms was given
in [13, 14]. As described in [13, 14] there is a general
coordinate transformation xm
i
from
¤ 4
¤
¤ 4 resulting in the metric tensor
gi k
xm
i xm
k (1)
where indices
,
= 1,...,8 and i, m, k = 1,...,4. The Einstein
summation convention is used, that is, indices occurring
twice are summed over.
gi k
:
,
1
8
gi k (2)
gi k
xm
i xm
k .
(3)
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 H
!
with
"=1,...,12 is used:
gi k
#
H
$&%
:
',
(
H
)
gi k (4)
where summation indices are obtained from the definition
of the hermetry forms. The expressions gi k H
are interpreted as different physical interaction pot$e ntials
caused by hermetry form H
*
, extending the interpretation
of metric employed in GR to the poly-metric
of
¤
8. 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.
3
Figure 1: In GR the metric tensor is computed using a mapping
from manifold M (curvilinear coordinates
,.-
) in spacetime
/
4 to manifold N in spacetime
/10
(Euclidean coordinates
xm). Calculating the components of the metric tensor as
well as lengths, areas, and volumes from the metric tensor a
mapping to the set of real numbers is needed [17]. This kind
of mapping delivers one type of metric tensor that is responsible
for gravity, appearing on the LHS of the Einstein field
equations.
2.2 Transformation Equations and Coupling
Constants
There are two equations describing the conversion of
photons into pairs of gravitophotons, Eqs. (5, 6). The
first equation describes the production of N2 gravitophoton
particles from photons.
wph
¤
r
wph
Nwgp
wph
¤
r
wph
Awph .
(5)
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.
(5, 6) is that an electromagnetic potential (photon) containing
probability amplitude Awph can be converted
into
a gravitophoton potential (pair of gravitophotons) with
associated probability amplitude Nwgp. From Eqs. (5, 6)
the following relation needs to be satisfied for gravitophoton
production, requiring the existence of a shielding
potential that has to be provided by experiment.
The function A(r) can be calculated from Landau's radiation
correction with numerical values for A ranging
from 10-3 to 10-4. From Eqs. (5) one obtains
Nwgp
Awph . (6)
4
Figure 3: In Heim space there are four additional internal
coordinates with timelike (negative) signature, giving rise to
two additional subspaces S2 and I2. Hence,
8 comprises four
subspaces, namely ¤ 3, 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.
H8
S2 S2 I2 I2
gik
9
3
gik
10
T1
gik
11
3 T 1
gik
g 12 ik
1
3
gik
2
T1
gik
3
3 T1
gik
4 gik
5
3
gik
6
T 1
gik
7
3 T 1
gik
8
Heim Space
In H8, there exists 12 subspaces, whose metric gives
6 fundamental interactions
(+ + + - - - - -)
signature of H8
Figure 4: There should be three gravitational particles,
namely the graviton (attractive), the gravitophoton (attractive
and repulsive), and the quintessence or vacuum particle
(repulsive), represented by hermetry forms H5, H11, and H12,
see Table 3.
Figure 2: 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
8,
having 8 dimensions. Although
8 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
, -
) in spacetime
/
4 to internal space
8
and back to manifold N in spacetime
/ 0
(Euclidean coordinates
xm) must be used to properly describe the physics. This
is a major deviation from GR and leads to a poly-metric. For
the construction of the poly-metric see Eqs. (2) and (4).
4
4
l
1, . . . ,4
!#"#$&%'(')+*#,$ -
1, . . . ,8
.*'/1032+,+!4* 56"+!7('8*#,)
m
1, . . . , 4
: 9
;
l
< -
xm
gik
=
Heim Polymetric
gik
>? >@
3 Heim-Lorentz Force for Space Propulsion
The Heim-Lorentz force derived in [13] 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. This issue is addressed in
Sec. 4.
3.1 Heim-Lorentz Force
Eqs. (7) and (8) are the so called Heim-Lorentz force
which is a gravitational force.
Fgp¤p e 0 vT H (7)
where p indicates that only proton and neutron absorption
processes were considered in [13, 14]. p
is determined as
32
3 Nwgpe
wph
2Nwgpa
4
mp c
2
d
d0
3 Z . (8) p (dimensionless) is a highly nonlinear function of the
probability amplitude of the gravitophoton particle.
It is important to note that Eq. (7) only describes the
acceleration stage of gravitophoton field propulsion.
There is a distance rN at which the shielded electric potential
produced by the nucleus and the magnetic potential
cancel, given by Eq. 30 in [13]
r N
Z e
Q
R
c
vi
c
vi
T . (9)
5
Figure 5: 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 experimental setup
also would serve as the field propulsion system, if appropriately
dimensioned. For very high magnetic fields over 30 T,
the current loop or solenoid must be mechanically reinforced
because of the Lorentz force acting on the moving
electrons in the solenoid, forcing them toward the center of
the loop.
I
N
B r
B I
r
Due to the shielding of the proton charges in the nucleus
by virtual electrons coming out of the spacetime
field (or vacuum), for distances r < rN, the atomic number
is a function of distance from the nucleus that is,
Z=Z(r). At distances rN smaller than the Compton wavelength
of the electron, the bare charge of the proton
gradually becomes visible, as expressed by A(r). From
Eq. (6) it is obvious that a value of A larger than 0 is
needed for gravitophoton production and from Eq. (9) it
can be seen that a small value of rN is obtained by high
velocities of the electrons in the current loop as well as
a high speed of the rotating torus. A more detailed
analysis for rN accounts for the fact that Q is not a point
charge. The value for rN turns out to be
r N
Z e c2
4 I n vi
T (10)
where I is the current and n is the number of turns in the
solenoid (not to be confused with n in Eq. (12)). A simple
calculation for a rotating torus having a mass of
1,000 kg of hydrogen and a spacecraft mass of 105 kg,
shows that a value of Nwgpe= 4.410-5 is needed, where
a magnetic induction of roughly 20 T is necessary for I
n = 4107, and d=0.5m, D=6 m, see Table 1. The velocity
of the torus is 700 m/s. The number of turns n
was assumed as 6.6104. These values should be compared
to Table 1. It should be noted that a torus of 6 m
requires a fairly large experimental setup. Alternatively
a smaller torus diameter requires a higher magnetic induction.
The kinetic energy provided to the torus is
2.45108 Joule which is substantial. However, it is a
small amount compared to a spacecraft having a mass
of 105 kg, flying at a speed of 1% of the speed of light,
which carries an energy content of 4.5´1017 J. Even if
the spacecraft can be provided with a 100 MW nuclear
reactor, it would take some 143 years to produce this
amount of energy.
In the end, a detailed power and mass analysis has to be
carried out to build the optimal field propulsion device.
It is not the value of the magnetic induction in the current
loop, but it is the strength of the magnetic field H
that is of importance. In other words, an iron core in a
magnetic coil will not increase the production of graviton
photon pairs from the vacuum. Hence, the value
¤ 0H is listed in Table 1.
d
[m]
D
[m]
I n
[An]
N wgpe
0H
(T)
0.2 2 6.6
106
10-
7 13
10-16
0.3 3 1.3
107 7.4
10-
6 18
10-5
0.4 4 2.7
107
27
1.1
10-
2
0.5 5 4
107
33 0.72
0.6 6 1.5
107
38 3
Table 1: From the Heim-Lorentz force the following values
are obtained. A mass of only 100 kg of the torus is assumed,
filled with 5 kg of hydrogen. The current density is 600
A/mm2. The value
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 ¤ 0H is the
magnetic induction generated 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 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 1¤ V/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.
3.2 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
4(n), in which covariant physical laws
with respect to
4 exist, is characterized by the scaling
transformation
xi
n
1
n2 x
1
,i
1,2,3 ; t
n
1
n3 t
1
v
n
n v
1
;c
n
n c
1
G
n
1
n
G ;
n
;n
.
(11)
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. (11) 4. In
other words, physical laws should be covariant under
discrete (quantized) spacetime dilatations
(contractions). There are two important questions to be
addressed, namely how the value n can be influenced
4 It is straightforward to show that Einstein's field
equations as well as the Friedmann equations are
also invariant under dilatations.
6
by experimental parameters, and how the back-transformation
from
4(n)
¤
4 is working. The result of the
back-transformation must not depend on the choice of
the origin of the coordinate system in
4. As a result of
the combined mapping from
4
¤
4(n)
¤
4 , the
spacecraft has moved a distance n v t when re-entering
4. The value t denotes the time difference between
leaving and reentering
4, as measured by an observer
in
4. This mapping for the transformation of distance,
time, and velocity differences cannot be the identity
matrix. That is, the back transformation from
4(n)
¤
4 is not the inverse of the mapping from
4
¤
4(n),
otherwise parallel space would have no physical meaning.
A quantity v(n)=nv(1), obtained from a quantity of
4, is not transformed again when going back from
4
(n) to
4, which means that the velocity of the spacecraft
is v(1) when returning to
4. This is in contrast to
a quantity like t(n) that transforms into T. The reason
for this non-symmetric behavior is that t(n) is a quantity
from
4(n) and thus is being transformed. The
spacecraft is assumed to make a transition from
4 into
4 (n) at velocity v (or ). Since energy needs to be conserved
in
4, the kinetic energy of the spacecraft remains
unchanged upon reentry.
The value of n is obtained from the following formula,
Eq. (12), relating the field strength of the gravitophoton
field, g+
gp, with the gravitational field strength, gg, produced
by the spacecraft itself,
n
¤
ggp
+
gg
Ggp
G
. (12)
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. (12) 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.
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 some 30 T, compare Table 1, a rotational speed
of the torus of vT = 103 m/s, and a torus mass of 2103
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
¤ 2d M
g , resulting
in a total flight time of 4 hours. A Mars mission,
under the same assumptions as a flight to the moon,
would achieve a final velocity of v= gt = 1.49106
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 3104 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
[14].
4 Technical Realization of Field Propulsion
System
From the discussion in Section 3.1 it has become clear
that a large magnetic field is needed to produce an appreciable
Heim-Lorentz force. In addition, Eq. (9)
shows that the velocity of the electrons in the current
loop must be large. Pulsed magnets can reach very high
magnetic field strengths up to 60 T (Sandia Laboratories),
and initially it was thought that these magnets
could be used to provide the magnetic field to generating
the Heim-Lorentz force needed for field propulsion.
Regarding the equation for the Heim-Lorentz force,
however, a high velocity of the electrons in the coil is
needed. It is not sure that using a pulsed magnetic field
this can be achieved in an effective way, since during
the pulse period electrons need to be quickly accelerated
to the speed vc of the Cooper pairs, see below. The
effectiveness of a pulsed magnet system depends critically
on the ratio of pulse time and acceleration time.
Furthermore, it is not clear how a rapidly time-varying
Heim-Lorentz force would act on the structure of the
spacecraft. A more detailed analysis would have to be
carried out. At present, the usage of steady magnetic
fields is preferred.
4.1 Heim Field Propulsion Device
If we look at the electron speed in metals, it is found
that electron velocity is proportional to the applied electric
field E. Electrons collide with the ions of the lattice
and the time
between these collisions is available to
accelerate the electron. A brief calculation shows that
s
For a field strength of E = 10 V/m one obtains
a speed of some 1 cm/s for the electron. Hence, no metallic
conductor in a non-superconducting state can be
used.
At critical temperature Tc some materials become superconductors
that is, their resistance goes to 0. Superconductors
have an energy gap of some Eg 3.5 kTc .
This energy gap separates superconducting electrons
below from normal electrons above the gap. At temperatures
below Tc , electrons are coupled in pairs,
called Cooper pairs, which are bosons. The exact formation
of Cooper pairs is not known. The coupling of
the electron pairs seems to be via phonons, generated
by electron movement through the lattice of the superconductor.
The size of a Cooper pair is some 103 nm.
The crystal lattice contains defects that lead to an energy
transfer
E from the electron gas to the lattice.
E
must be smaller than Eg otherwise the Cooper pairs are
destroyed.
7
The speed of the Cooper pairs can be calculated in a coordinate
system where the electron gas is at rest and the
lattice is moving, applying classical energy and momentum
conservation. Decelerating the grid means that
Cooper pairs gain energy. The maximum amount of energy
that a Cooper pair can absorb is Eg , otherwise it is
lifted in the band above, and superconductivity is lost.
Therefore the simple ansatz
1
2
mvc
2
Eg
3.5 k T c (13)
can be used, vc denoting the velocity of a Cooper pair.
At temperature Tc = 10 K a speed of vc = 104m/s is obtained.
4.2 Magnetic Field Generation
In order to obtain a viable space propulsion system the
Heim-Lorentz formula requires magnetic fields of several
tens of Tesla and current densities of several hundred
A/mm2. It is an experimental fact that high density
magnetic fields destroy superconductivity. Type I (metals)
superconductors have small BC. Type II (alloys) superconductors
have higher BC. The picture, Fig. 7, plotted
from data taken from the internet, shows the critical
current density, j
¤
2en v , at 4.2 K (He). At 25 T a
current density of some 448 A/mm2 can be sustained,
which comes close to the value of 600 A/mm2 assumed
for field propulsion. Values of 60 T, needed to transit
into parallel space, so far have not been reached.
In the following, a brief discussion on the state of the
art of producing high magnetic fields is given. For the
fusion reactor Iter to be built in France in the next decade,
a magnetic field strength of 9.7 T at 4.5 K carrying
a current of 80 kA using a 316LN stainless steel jacket
with a diameter 40.7 mm was reached. This magnetic
field is, however, not large enough for field propulsion.
There is a new high temperature superconducting material
available, Nb3Sn, that has reached 12 T with 3,000
A/ mm2 at 4.2 K. Other suitable compounds are Bi-
2212, Bi-2223, and Y-123.
High field magnets need a careful mechanical design
because the Lorentz forces scale with B2. Nb3Sn can
withstand up to 150 MPa compressive force. In principle,
a large current is better since lower number of turns
is needed and therefore lower self-inductance.
This also means better superconductor volume efficiency
or lower stored energy and thus lower peak temperature.
However, the brittle Nb3Sn superconductor
material is difficult to be made into long wires.
Conclusions
In GR the geometrization of spacetime gives rise to
gravitation. In Heim's theory 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.
In this way 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. 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.
The technology for magnetic field generation seems to
be sufficient to measure the Heim-Lorentz force, since
a magnetic field of 18 T is feasible, but it must be provided
over a diameter of some 3 m, according to Table
1 to measuring a change in acceleration of 2 10-5.
The goals of advanced propulsion as laid down by
NASA in [15] are still valid and can only be obtained
by novel physics.
8
Figure 7: In this figure the current desity versus magnetic
field at a temperature of 4.2 K (LHe) is plotted. At
25 T a current density of 448 A/mm2 can be supported, a
value that comes close to the 600 A/mm2 needed for field
propulsion.
0 5 10 15 20 25
200
400
600
800
1000
1200
1400
10
15
20
25
30
35
40
45
JE (A/mm 2)
JE(A/mm2)
n-value
n-value
At 4.2K, 25T:
IC = 224 A
JE = 448 A/mm2
n-value = 16
Applied Magnetic Field (T)
FutureWork
Needless to say that Heim theory and also LQT harbor
many unresolved issues. Heim theory needs to be put
on a more rigorous mathematical basis. For instance, it
is well known that Einstein's equations of general relativity
can be derived from the variation of the Einstein-
Hilbert action. In the same way it needs to be shown
how the hermetry forms can be used to derive all other
known fundamental interactions. In particular, it should
be clarified how the two additional gravitational interactions
can be derived from a modified Einstein-Hilbert
action. The conversion equation from photons into
gravitophotons as well as the conversion of gravitophotons
and gravitons into quintessence particles needs to
be mathematically proved. So far, the authors have not
derived the so called mass formula that is an eigenvalue
equation leading to the mass spectrum of elementary
particles as given by Heim.
With regard to the high currents needed, an alternative
could be to use a hot plasma. Since currents of some
5107 A are needed, this seems to be out of reach at
present.
ACKNOWLEDGMENT
The authors are most grateful to Prof. P. Dr. Dr. A.
Resch, director of IGW at Innsbruck University, for his
continuous support in writing this paper. The second
author was partly funded by Arbeitsgruppe Innovative
Projekte (AGIP) and by Efre (EU)at the Ministry of
Science and Education, Hanover, Germany.
Special thanks for help go to the friendly staff at the
Loews Ventana Canyon Resort, Tucson, AZ where part
of this paper was written.
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9
10
Generated by Messenger particles Force Coupling constant
real particles graviton attractive Gg
virtual particles
gravitophoton repulsive and attractive
Ggp
+ ,Ggp
-
¤ 1672
Planck mass
vacuum
quintessence or vacuum
particle
repulsive Gq=4.3565
10-18 G
TABLE 2. The three gravitational interactions are related to different types of matter. The coupling constants were calculated
using an idea by Heim.
TABLE 3. Classification scheme for physical interactions and messenger particles obtained from poly-metric in Heim space
8. Further explanation is given in the paper. Superscripts on subspaces indicate dimension. Subspaces S2 and I2 stand for organization
and information, respectively. A hermetry form characterizes either a physical interaction or a messenger particle,
and is associated with an admissible subspace. Either S2 or I2 need to be present in such a subspace in order to realize a
physical event in our spacetime. Spaces R3, T1, S2 and I2 form the basis of Heim space 8. The additional four dimensions
of are not needed for describing physical interactions, but seem to steer probability amplitudes.
Subspaces Hermetry form Messenger
particle
Symmetry group Physical
interaction
3 H1 3 , I 2
gluons SU(3) strong
3
R3 ,T 1
T 1
H4 3 , S2 , I 2
H3 3 ,T 1 , S2 , I 2
H5 T 1 , S2 , I 2
Z0 boson
W
bosons
photon
O
3
U
1
SU 2
U 1
electroweak
T 1 H5 T 1 , S2 , I 2
photon U(1) Lorentz force
S2 H12 S2
graviton O(2)[=U(1)] gravity
S2
S2 , I 2
I 2
H11
- S2 , I 2
H11 S2 , I 2
H11
+ S2
, I 2
-, neutral , +
gravitophotons
O
2
U
1
O 2
O 2
=
U 1
U 1
Heim-Lorentz
force
I 2 H10 I 2
vacuum particle
(quintessence)
[O(2)]=U(1) vacuum
