AIAA 2006-4608 SPACETIME PHYSICS AND ADVANCED PROPULSION CONCEPTS
13/05/2014 20:09
AIAA 2006-4608
SPACETIME PHYSICS AND
ADVANCED PROPULSION CONCEPTS
Walter Dröscher1, Jochem Hauser1,2
1Institut für Grenzgebiete der Wissenschaft, Innsbruck, Austria
and
2Faculty Karl-Scharfenberg, University of Applied Sciences, Salzgitter, Germany
Short Version
Abstract: Spacetime physics includes general relativity (GR), quantum theory, quantum gravity, string theory (additional external
dimensions), and gauge theory (additional internal dimensions) as well as some modern variations. The paper will discuss
the requirements on future propulsion systems stemming from the demands for routine missions to LEO, the moon, or
planetary missions within the solar system, as well as interstellar flight. These requirements are compared with the limits imposed
by the physical laws of GR in conjunction with the physical theories listed above. The physical consequences of these
field theories in curved-spacetime as well as string and gauge theory, are discussed. Moreover, recent developments in the
structure of spacetime are presented, and their consequences for advanced propulsion systems are outlined. In particular, a
novel experiment (ESA, March 2006) reporting about the generation of an artificial gravitational field in the laboratory is discussed.
This experiment, if confirmed, could serve as the basis for a field propulsion device. Since a thorough understanding
of the underlying physical principle is of prevailing importance, a detailed theoretical analysis of this experiment is presented.
Utilizing the experimental data along with the insight gained from theoretical considerations, a concept for a field propulsion
device is developed. Preliminary results on the capability of this device will be given. Finally, an outlook of the necessary experimental
and theoretical prerequisites is given to both understand the novel physics as well as the technical requirements for
such a propulsion device.
1 Senior scientist, 2 Senior member AIAA, member SSE, © IGW, Innsbruck, Austria 2006
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1 Spacetime and Space Propulsion2
Space flight within the solar system requires the covering
of large distances. The distance to our moon is some
3.8×105 km, while Mars, our favorite destination is some
0.5 A.U. away (astronomical units, 1 A.U. = 1.5×108 km).
The next planet, Jupiter, is already some 4 A.U. away
from Earth. The closest star is Proxima centauri, which is
1.30 pc away from earth (parsec, 1pc = 3.3 ly) or, using
lightyear, the distance light travels in the time of 1 year,
(1 ly = 9.46×1012 km), it would take the light some 4.3
years to reach this star. Expressed in miles, the distance is
some 25 trillion miles from earth. The star closest to us
which is similar to our sun with respect to size and surface
temperature is Centauri, some 1.33 pc away. But
these distances are small when compared to the dimension
of the Milky Way Galaxy which comprises a galactic
disk of some 100,000 ly in diameter and some 4,000 ly
for the galactic bulge. Our solar system is located some 8
kpc (kilo parsec) from the galactic center. Our galaxy
contains some 100 billion stars, and the universe contains
some 100 billion galaxies. The farthest of these galaxies
is some 13 billion ly away, which is roughly the size of
the observable universe. The age of the Earth is estimated
to be some 4.5 billion years, while there are stars that are
7 to 10 billion years old. Having mentioned both distance
and time, the concept of spacetime has been utilized and
also, implicitly, the concept of metric has been employed
to measure distances in this four-dimensional spacetime.
This is the environment in which spaceflight has to take
place.
Next, we will briefly discuss our current capabilities 3 to
travel through space and time that is, in spacetime. Current
space transportation systems are based on the principle
of momentum generation, regardless whether they are
chemical, electric, plasma-dynamic, nuclear (fission) or
fusion, antimatter, photonic propulsion (relativistic) and
photon driven (solar) sails, or exotic Bussard fusion ramjets,
solar sails, nuclear explosions (pusher, Orion), antimatter
propulsion are most likely in the realm of unfeasible
technologies because of the large engineering and/or
safety problems as well as their prohibitively high cost.
The specific impulse achievable from thermal systems
ranges from some 500 s for advanced chemical propellants
(excluding free radicals or metastable atoms), some
2 Invited paper in the session 50-NFF-3 Faster Than Light, AIAA 42nd
Joint Propulsion Conference, Sacramento, CA, 9-12 July 2006. A
more detailed paper will be available at the conference.
3 The cover picture shows a combination of two pictures. The first one,
taken from ref. [1], shows a view (artist's impression) from an existing
planet orbiting the solar-type star HD 222582 some 137 ly away.
The second one depicts the principle of the propulsion system used to
reach this planet, see Fig. 3.
1,000 s for a fission solid-core rocket (NERVA program
[2]) using hydrogen as propellant (for a gas-core nuclear
rocket specific impulse could be 3,000 s or higher but requiring
very high pressures) up to 200,000 s for a fusion
rocket [3]. Although recently progress was reported in the
design of nuclear reactors for plasma propulsion systems
[4] such a multimegawatt reactor has a mass of some
3×106 kg and, despite high specific impulse, has a low
thrust to mass ratio, and thus is most likely not capable of
lifting a vehicle from the surface of the earth. With regard
to fusion propulsion, the gasdynamic mirror has been proposed
as highly efficient fusion rocket engine. However,
recent experiments revealed magneto-hydrodynamic instabilities
[5] that make such a system questionable even
from a physics standpoint, since magnetohydrodynamic
stability has been the key issue in fusion for decades. The
momentum principle combined with the usage of fuel, because
of its inherent physical limitations, will not allow
going to routine spaceflight. The above discussion does
not even consider the difficulties entered when the simplicity
of the physical concept meets the complexities of
the workable propulsion system.
At relativistic speeds, Lorentz transformation replaces
Galilei transformation that is, the rest mass of the propellant
is multiplied by the factor (1 - v2/c2) that goes to infinity
if the exhaust velocity v equals c, the speed of light
in vacuum.
For instance, a flight to the nearest star at a velocity of
some 16 km/s would take about 80,000 years. If the speed
of light cannot be transcended, interstellar travel is impossible.
We conclude with a phrase from the recent book on
future propulsion by Czysz and Bruno [6] : If that remains
the case, we are trapped within the environs of the
Solar System. In addition, the current state of propulsion
does not allow either convenient interplanetary travel and
inflicts prohibitively high cost even for low earth orbits.
As mentioned by Krauss [7], general relativity (GR) allows
metric engineering, including the so-called warp
drive, see Sec. 2.2, but superluminal travel would require
negative energy densities. Furthermore, 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
GR and QM (quantum mechanics). Second, not
even the question about the total number of fundamental
interactions can be answered. Hence, the goal to find a
unified field theory is a viable undertaking, because it
2
might lead to novel physics, which, in turn, might allow
for a totally different principle in space transportation.4
2 Classical Spacetime
In GR the model of space and time supports continuous
and differentiable functions and provides a structure that
has the same local topology as ℝ4. Therefore, spacetime is
a topological space and thus comprises a collection of
open sets. For small regions it is assumed that the open
sets possess the topology of ℝ4. Therefore, a one-to-one
mapping exists between the open set of spacetime and ℝ4.
Each point in spacetime has a unique image in ℝ4 and vice
versa.
2.1 Spacetime as a Manifold
Equipped with the features described above, spacetime is
called a manifold. In general, physical fields defined on
an open set of this manifold are assumed to be differentiable.
Spacetime thus is considered to be a multiply differentiable
manifold. However, as will be shown in Sec. 3,
spacetime must be quantized. Therefore, it is not generally
possible to have a third point between any two points
in spacetime. Spacetime is not dense and hence the concept
of manifold is incorrect, at least on the Planck
length, see below. In SRT (special theory of relativity)
Lorentz contraction is continuous, but this contradicts the
concept of minimum length.
At Planck scales SRT cannot be correct. GR uses the concept
of curvature, but at Planck scales it cannot be measured
exactly. This is equivalent to fluctuations of curvature
and thus of gravitation itself. A unified field theory
describing all physical interactions by individual metrics
would be subject to fluctuations as well that is, all physical
forces would be subject to these fluctuations.
Physics is not possible below the Planck scale, since concepts
of metric, dimensionality, or points are not defined.
Spacetime itself is a field and thus needs to be quantized,
leading to quantum gravity (QG), see, for instance [8]. So
far, QG has not lead to a unified field theory, and does not
predict phenomena that could lead to a novel propulsion
concept. Conventional wisdom claims that quantized spacetime
acts on the Planck scale only. On macroscopic
scales the concepts of GR are sufficient to describe spacetime.
However, this argument may turn out to be invalid,
since despite the smallness of the quantized action, denoted
by the Planck constant ℏ, physical phenomena on the
macroscopic scale do occur, for instance superconducting.
Therefore, it is possible that a quantized spacetime will
lead to observable physical phenomena. A quantized spacetime
together with the prediction of a repulsive gravitational
force, predicted by the unified theory presented,
Sec. 3.2, leads to the concept of hyperspace (or parallel
space) in which the limiting speed of light is nc, with n >
1, integer and c the vacuum speed of light [9], [10].
4 A more detailed discussion will be given in our paper entitled Field
Propulsion I: Novel Concepts for Space Propulsion.
2.2 The Physics of Continuous Spacetime
Einsteinian spacetime [11], [12] is indefinitely divisible
and can be described by a differentiable manifold. In reality,
however, spacetime is a quantized field. Gra-vitation
is the dominant force in systems on astronomical scales.
GR can be summarized in the single sentence: matter
curves spacetime. For a flat geometry, the angles of a triangle
add up to 180 degrees. The spacetime metric of a
flat universe is given by
ds2=dx2¤dy2¤dz2−c2dt2 .
On the surface of a sphere spherical coordinates are used
ds2=dr2¤r2d ¤2¤r2sin2¤d ¤2−c2dt2 .
For a generally curved spacetime the metric is written in
the form (double indices are summed over)
ds2=g¤¤dx¤dx¤
where g¤¤ is the metric, x1, x2, x3 are the spatial coordinates,
and x4 is the time coordinate 5. The cosmo-logical
principle states that the Universe does not have preferred
locations (homogeneous) or directions (isotropic). Therefore
the spatial part of the metric has constant curvature.
Extending the spherical metric, the most general metric is
given by the Robertson-Walker metric
ds2=a2 ¤t ¤[ dr2
1−k r2¤r2 ¤d ¤2¤sin2¤d ¤2¤]−c2dt2 ,
where a(t) is the scale factor of the Universe. Here it is
assumed that the Universe started from a fixed size x0 and
expanded according to a(t). Two points that were at distance
x0 at time t0, now are at distance x(t) = a(t) x0.
In 1994 Alcubierre [13], [14] specified the following metric,
termed the warp-drive spacetime
ds2=[dx2−V s f ¤ rs¤dt2¤dy2¤dz2]−c2dt2 ,
where Vs(t) is the velocity along a given curve xs(t) 6 and
r2
s(t) = (x-xs(t))2 + y2 + z2. A choice for fs(t) is fs = (1-rs/R)4
and R is a distance. Without proof it is stated that, if this
warp-drive metric could be generated - the term metric
engineering was coined - around a spaceship, the vehicle
would be traveling faster than the speed of light, seen
from a spacetime diagram of flat space. Locally the ship
is moving less than the speed of light. A bubble of spacetime
curvature must surround the spaceship. Since the Alcubierre
metric requires a negative local energy density, it
cannot work in GR. Quantum mechanics allows negative
energy density, and perhaps a combination with the quintessence
particle, see Fig. 2, the sixth fundamental force
predicted by EHT. It is interesting to note that the experi-
5 Often the time coordinate is denoted as x0.
6 For simplicity y = 0 and z = 0 are assumed.
3
ment by Tajmar et al. [15] could be interpreted as metric
engineering since an artificial gravitational field was generated
and, as a result, the local metric has been changed.
There are also spacetime concepts of higher dimen-sionality.
Kaluza (1921) introduced an additional fourth spatial
dimension into Einstein's field equations, and in a letter
to Einstein pointed out that Maxwell's theory of electromagnetism
was comprised in the now 5-dimen-sional
Einstein equations. However, his theory produced divergencies
and could not answer the question about the visibility
of this 5th dimension. In 1926 Klein, a Swedish
physicist, introduced the concept of a curled up dimension
that exists on the Planck length scale only, and thus
cannot be observed by experiment. String theory [16], see
Sec. 3.1, has extended this concept by intro-ducing 8 additional
spatial dimensions, resulting in a total of 11 spatial
dimensions.
3 Quantized Spacetime
In the following it is shown that the combination of
quantum theory (Heisenberg's uncertainty relation) with
special relativity (constancy of the speed of light and
E = m c2) and general relativity (Schwarzschild radius)
directly leads to a quantized spacetime, resulting in the
well known Planck scales. The proof is straightforward
and is given below. The quantization of spacetime leads
to the proposition of a hyperspace (parallel space) in
which superluminal speeds should be possible, see [17].
Heisenberg´s indeterminacy (uncertainty) relation, for instance
relating time and energy indeterminacies,
¤t¤E¤ℏ , allows for arbitrarily small Δt by making
the energy uncertainty arbitrarily large. However, this is
not the case in the real physical world. It is straight-forward
to prove the discreteness of spacetime. To this end,
the time measurement process using clocks is analyzed
[18]. Einstein's GR itself is used to disprove the existence
of continuous spacetime. According to Einstein, the energy
of any material object is E = mc2. The smallest time
interval, δt, that can be measured must of course be larger
than the time uncertainty required to satisfy Heisenberg's
uncertainty relation that is ¤t¤¤t=ℏ/¤E. A clock of
mass m cannot have an energy uncertainty ΔE > mc2, because
this would lead to the creation of additional clocks,
hence ¤t¤¤t=ℏ/mc2 . A clock of length l needs a
measuring time c δt > l in order to receive the measuring
signal. A characteristic length of a material body is its
Schwarzschild radius, namely when its gravitational energy
equals its total energy mc2, i.e., rS = Gm/c2. This
means for the mass of the clock m < rS c2/G, because the
body must not be a black hole from which signals cannot
escape. Inserting the value l for rS , m < δt c3/G. Inserting
the value of m in the above relation for δt, one obtains the
final relation ¤t2¤ℏG/c5. Thus the quantization aspect
of the GODQ principle, which comprises the four basic
physical principles of Nature, see Sec. 3.2.1, directly
delivers a fundamental lowest limit for a time interval,
termed the Planck time. In a similar way the smallest
units for length and mass can be found. As shown above,
Planck units are constructed from the three fundamental
constants in Nature, namely ℏ, c, and G. The values for
the Planck units are:
• Planck mass mp = (c/G)1/2 = 2.176 ´ 10-8 kg,
• Planck length lp = (Gℏc-3)1/2 = 1.615 ´ 10-35 m,
• Planck time tp = (Gℏ/c5)1/2 = 5.389 ´ 10-44 s.
This means that the classical picture of points in a continuous
spacetime does not make physical sense. Physics below
the Planck units is not possible, since one cannot distinguish
between vacuum and matter. No measurements
are possible. The nature of spacetime is discrete in the
same way as energy is discrete, expressed by E = h¤.
Since spacetime therefore is a quantum field, it should
have corresponding quantum states, described by a quantum
field theory. Since spacetime is equivalent to gravity,
gravity itself needs to be described by a quantum field
theory. In both classical physics and quantum mechanics
point particles are used, and the inverse force law leads to
infinities of type 1/0 at the location of the particle. As was
shown above, any particle must have a discrete geometric
structure, since it is finite in size. The minimal surface
must be proportional to the Planck length squared. From
scattering experiments, however, it is known that many
particles have a much larger radius, for instance, the proton
radius is some 10-15 m, and thus its surface would be
covered by about 1040 elemental Planck surfaces. Hence,
an elementary particle must be a highly organized and
also complex geometrical structure. It is therefore mandatory
that point particles are banished. In addition, the organizational
state of an entity or structure needs to be
measured and therefore, among other reasons, the concept
of an organization coordinate in an internal space (de-
4
Figure 1: This picture, taken from Wikipedia, shows
three types of possible geometries for the Universe,
namely closed, open, or flat. At present, a flat Universe
is assumed.
scribing the additional degrees of freedom) is introduced,
see Sec. 3.2.1.
3.1 Spacetime of Higher Spatial Dimensions:
String Theory
The theory by Kaluza and Klein (1921, 1926) already introduced
a fourth spatial dimension to account for electromagnetism.
According to string theory, electrons are not
point particles, but are vibrations of a string, whose length
is at the Planck scale, some 10-35 m. Strings are one-dimensional
entities. Modifying the vibrations frequency of
these strings they can turn into other particles, for instance,
the electron can turn into a neutrino, or into any of
the known subatomic particles. String theory leads to a
unification of the four fundamental interactions, but requires
11 real spatial dimensions, [16]. However, because
of the discrete nature of spacetime there seems to be no
need for string theory, which replaces point particles by
strings, but requires hitherto unobserved additional spatial
dimensions.
However, there is a fundamental difference compared to
the concept of spacetime with internal dimensions, in that
strings are objects in spacetime, while in the next section
a geometrization concept is employed that explains all
particles as geometric objects constructed from spacetime
itself.
3.2 Spacetime with Internal Dimensions
However, there exists another concept, coming from the
idea that elementary particles have additional degrees of
freedom in some kind of internal space. Therefore, the
concept of physical space as the combination of spacetime
and internal space is introduced. This marriage of 4-
dimensional spacetime with internal space is called fiber
bundle space mathematically. In the following the term
physical space will be used for this combination, since
all the fundamental forces of physics will be described in
this space. These internal degrees of freedom can then be
connected with the dynamical motion in spacetime. This
is the geometrical structure utilized in gauge theory. The
dimension of the internal space and its symmetries determine
the physics that is possible. In order to have a unified
field theory the proper internal space has to be constructed
that encompasses all interactions of physics. In
the next section, GR is equipped with an 8-dimensional
internal space (all internal coordinates have negative signature),
termed Heim space. Once this internal space is
included, all physical interactions are fixed. There is only
one single selection rule used to selecting internal subspaces.
It turns out that six fundamental physical interactions
should exist.
3.2.1 Extended Heim Theory
In EHT a set of 8 additional coordinates is introduced, but
contrary to String theory, the theory postulates an internal
space with 8 dimensions that governs physical events in
our spacetime (actually a manifold M4 ).The crucial point
lies in the construction of the internal space that should
come from basic physical assumptions, which must be
generally acceptable. In EHT, an 8-dimensional space is
constructed, termed Heim space, H8 that is missing in GR.
In other words, GR does not possess any internal space,
and thus has a very limited geometrical structure, namely
that of pure spacetime. Because of this limitation, GR
cannot describe the fundamental forces in physics and
consequently has to be extended. The extension as done
in EHT, lies in the introduction of the internal space H8.
EHT reduces to GR when this internal space is omitted.
The metric tensor, as used in GR, has purely geometrical
means that is of immaterial character only, and does not
represent any physics. Consequently, the Einsteinian Geometrization
Principle (EGP) is equating the Einstein
curvature tensor, constructed from the metric tensor, with
the stress tensor, representing energy distribution. Stated
in simple terms: matter curves spacetime. In this way, the
metric tensor field has become a physical object whose
behavior is governed by an action principle, like that of
other physical entities.
Figure 2: EHT has, as one of its most important consequences,
the prediction of two additional, gravitational like interactions
and the existence of two messenger particles, termed
gravitophoton and quintessence.
According to the quantization principle, the minimal
length in the space part of H8 is the Planck length. Applying
the geometrization rule of the GODQ principle, see
below, Planck mass and Planck time are converted into
length units leading to two additional lengths constants
lpm = ħ/mpc and lpt = ctp that have the same numerical value
as lp but define two additional different length scales,
relating lengths with time units as well as length with
mass units. The introduction of basic physical units is in
contradiction to classical physics that allows infinite divisibility.
As a consequence, measurements in classical
physics are impossible, since units cannot be defined.
Consequently, Nature could not provide any elemental
building blocks to construct higher organized structures,
which is inconsistent with observation. Thus the quantiza-
5
tion principle is fundamental for the existence of physical
objects. Therefore the three Planck length units as defined
above must occur in the structure of both spacetime and
internal space H8. In spacetime length unit lp is the basic
unit for the spatial coordinates and lpt measures the time
coordinate. In order to connect geometry with physical
entities, in the internal symmetry space coordinates ¤i
are measured in units of lpm. Hence all lengths in H8 are
represented by multiples of 1/mp, and therefore internal
coordinates ¤i are denoted as energy coordinates. In
other words, the concept of energy coordinate ensures
that an inverse length is representing a physical mass.
Since length values are quantized, the same holds for
physical mass. In this regard the connection of geometry
with physical objects has been established, but, in order to
achieve this goal, the quantization principle had to be introduced
ab initio.
In contrast to Einstein, EHT is based on the following
four simple and general principles, termed the GODQ
principle of Nature7.
i. Geometrization principle for all physical interactions,
ii. Optimization (Nature employs an extremum
principle),
iii. Dualization (duality, symmetry) principle (Nature
dualizes or is asymmetric, bits),
iv. Quantization principle (Nature uses integers
only, discrete quantities).
From the duality principle, the existence of additional internal
symmetries in Nature is deduced, and thus a higher
dimensional internal symmetry space should exist, which
will now be determined.
In GR there exists a four dimensional spacetime, comprising
three spatial coordinates, x1, x2, x3 with positive signature
(+) and the time coordinate x4 with negative signature
(-). It should be remembered that the Lorentzian metric of
ℝ4 (actually spacetime is a manifold M4) has three spatial
(+ signature) and one time-like coordinate (- signature)
[19]. The plus and minus signs refer to the metric that is,
the spatial components are taken to be positive and the
time coordinate is negative. Therefore, the squared proper
time interval is taken to be positive if the separation of
two events is less than their spatial distance divided by c.
Hence a general coordinate system in ℝ4 (M4) comprises
the curvilinear coordinates8 xm with m=1,..,4. Next, the coordinate
structure of H8 is determined. Coordinates in H8
are denoted as ¤i , and are termed internal coordinates
with ¤=1,¤, 8. This set of 8 coordinates will now be
7 This will be discussed in detail in our forthcoming paper: Field propulsion
I: Novel Physical Concepts for Space Propulsion.
8 coordinates xμ can also be Cartesian. Meaning of coordinates will be
clear from the context.
determined by utilizing the GODQ principle introduced
above. To this end, the second law of thermodynamics is
considered, which predicts the increase of entropy. Everywhere
in Nature, however, highly organized structures
can be found like galaxies, solar systems, planets, plants
etc., which, according to the duality principle, have to be
introduced into a unified theory. A description of Nature
that only provides a route to decay or to lower organizational
structures is in contradiction to observation. Therefore,
an additional, internal (negative signature-) coordinate,
termed entelechial coordinate, ¤5 , is introduced.
The entelechial dimension can be interpreted as a measure
of the quality of time varying organizational
structure (inverse or dual to entropy). It should be mentioned
that all other additional internal coordinates have
negative signature, too. Second, when the universe was
set into motion, it followed a path marked by a state of
great order. Therefore, to reflect this generic behavior in
Nature, the aeonic dimension, ¤6 , is introduced that is
interpreted as a steering coordinate toward a dynamically
stable state. On the other hand, the entropy principle
is firmly established in physics, for instance in
¤- decay. Entropy is directly connected to probability,
which in turn is related to information. Therefore, two additional
coordinates ¤7 ,¤8 are needed, which are complementary
to the organizational coordinates, to reflect
this behavior of Nature, termed information coordinates
that are describing information waves. Finally, since both
space and time are essential in the evolution and decay of
structures, the internal symmetry space possesses a total
of 8 coordinates. In summary, coordinates ¤¤ with
¤=1,¤, 4 denote spatial and temporal coordinates,
¤¤ with ¤=5, 6 denote entelechial and aeonic coordinates,
and ¤¤ with ¤=7,8 denote information coordinates
in H8. The name gravitophoton has been chosen
because of the type of interaction, namely a transformation
of the electromagnetic field (photon) into the gravitational
field (gravitophoton). The arrow between the
gravtitophoton and electromagnetic boxes indicates the
interaction between the messenger particles that is, photons
can be transformed into gravitophotons. In the same
way the quintessence interaction can be generated from
gravitons and positive gravitophotons (repulsive force).
Heim space, H8 comprises four subspaces, namely ℝ3, T1,
S2, and I2. In the set of metric-subspaces that can be constructed,
where each element is denoted as a hermetry
form. Each hermetry form has a direct physical meaning,
for details see refs. [9], [20]. In order to construct a hermetry
form, either internal space S2 or I2 must be present.
In addition, there are three degenerated hermetry forms
that describe partial forms of the photon and the quintessence
potential. They allow the conversion of photons
6
into gravitophotons as well as of gravitophotons and
gravitons into quintessence particles. There exist 15 hermetry
forms, six of them describe the messenger particles
of the fundamental interactions. Hermetry forms H5,
H11, and H12 are used to describe the gravitational messenger
particles. In a very recent announcement by the
European Space Agency, 23 March 2006, the measurement
of an artificial gravitational field was reported, generated
by a rotating superconducting ring.
4 Propulsion Concepts from Spacetime
Physics
4.1 Metric Transformation (Transmutation)
In a recent experiment, funded by the European Space
Agency and the Air Force Office of Scientific Research,
Tajmar et al. ref. [15] report on the generation of a toroidal
(tangential, azimuthal) gravitational field in a rotating
accelerated (time dependent angular velocity) superconducting
ring. This would be the first time that an artificial
gravitational field is generated and, if correct, would have
great impact on future technology. Furthermore, the experiment
would demonstrate the conversion of electromagnetic
interaction into a gravitational field. This is exactly
the effect that is predicted by EHT, and both a qualitative
and quantitative explanation of this effect will be
given below. Since the experiment generates a tangential
gravitational field, it cannot be used directly as a propulsion
system. It is, however, of great importance, since it
shows for the first time that a gravitational filed can be
generated other than by the accumulation of mass. In this
section we will also discuss the validity of the physical
explanation, namely the Higgs mechanism to be responsible
for the graviton to gain mass, given by Tajmar and de
Matos [15], which they termed the gyromagnetic London
effect. According to these authors, this effect is the physical
cause for the existence of the measured gravitational
field.
The arguments of these authors are ingenious, but there is
some doubt whether the linearized Einstein equations, see
Eqs. (1, 2), can be used in the explanation of this effect.
Although these equations are predicting such a phenomenon,
the effect is 20 orders of magnitude smaller than the
observed one, and thus would be completely unobservable.
In the derivation, a magnetic field is set equivalent
to a gravitational field. This assumption of transforming a
magnetic field into a gravitational field is not compatible
with current physics.
Instead, the Heim-Lorentz force, as predicted by EHT but
now using a coupling to bosons (Cooper pairs), is used to
explain this effect. Deriving this effect from gravitophoton
interaction, a physical interpretation can be given that
explains both qualitatively and quantitatively the experimental
results. Moreover, theoretical considerations obtained
from EHT lead to the conclusion that a modified
experiment will generate a gravitational field acting
parallel to the axis of rotation of the ring (torus), see
Fig. 3, and thus can serve as a field propulsion principle9.
In this experimental configuration the superconducting
rotating ring is replaced by an insulating disc and a set
of superconducting coils as depicted, in principle, in Fig.
3. EHT allows to calculate the acceleration force and also
provides the guidelines for the construction of a propulsion
device. The actual experimental setup differs from
the simple configuration of the cover picture, but the principle
remains unchanged. According to the predictions of
EHT experimental requirements, i.e., magnetic field
strength, current densities and number of turns of the solenoid,
are substantially lower than for fermion coupling
that was assumed in all our papers so far, see refs. [9],
[10], [20].
Figure 3: The picture shows the physical principle of the experimental
setup to generate a gravitational field in the z-direction
(upward, above rotating disk) by the Heim-Lorentz
force using a superconducting coil (boson coupling) and a
rotating disk or ring. The actual experiment would be somewhat
different.
The superconducting current loop (blue), see Fig. 3, provides
an inhomogeneous magnetic field at the location of
the rotating disk (red). The z-component of the gravitophoton
field, bz is responsible for the gravitational field
above the disk. This experimental setup also serves as the
field propulsion device, if appropriately dimensioned.
4.1.1 Description of the Gravitomagnetic Field
Experiment
The materials for which a strong gravitational acceleration
was measured were niobium (Nb, TC=9.4 K) and lead
(Pb, TC = 7.2 K). No gravitational field was measured in
YBCO (Yttrium barium copper oxide, YBa2Cu3O7-x, TC =
94 K) and BSCCO (Bismuth strontium calcium copper
oxide, Bi2Sr2CanCun+1O2n+6, TC=107 K) which are so
called high-temperature superconductors whose critical
9 A detailed discussion will be given in our forthcoming paper entitled
Artificial Gravitational Fields.
7
I
r
N
z
¤ ¤
Br
BI
e¤z
e¤r
e¤¤
current density is substantially lower than that for Nb or
Pb.
Considering the Einstein-Maxwell formulation of linearized
gravity, a remarkable similarity to the mathematical
form of the electromagnetic Maxwell equations can be
found. In analogy to electromagnetism there exist a gravitational
scalar and vector potential, denoted by ¤g and Ag,
respectively, see [21]. Introducing the gravitoelectric and
gravitomagnetic fields
e=−∇¤g and b=∇×Ag (1)
the gravitational Maxwell equations can be written in the
form
∇⋅e=−4¤G¤ ,∇⋅b=0
∇×e=0 ,∇×b=−16¤G
c2 j
(2)
where j=¤ v is the mass flux and G is the gravitational
constant10. The field e describes the gravitational field
form a stationary mass distribution, whereas b describes
an extra gravitational field produced by moving masses.
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 be-
10 Here no consideration is given to the fact that G comprises three
parts according to EHT.
low 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.
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 Egap , otherwise it is lifted in the
band above, and superconductivity is lost. Therefore the
simple ansatz for the maximum energy gap
1/2mvc
2=Egap=3.5 k T c can be used, vc denoting the
velocity of a Cooper pair. At temperature Tc = 10 K a
speed of vc = 104 m/s is obtained. A smaller band gap
therefore cause a decrease in the speed of the Cooper
pairs. Quantum mechanics calculations yield a more correct
value of some vc = 105 m/s.
4.1.2 Field Propulsion
Fig. 3 describes the experimental setup for which an insulating
disk rotates above a superconducting solenoid. Fig.
4 depicts the experiment of Tajmar et al., where a superconducting
ring is subject to angular acceleration. In both
cases a gravitophoton force arises. EHT makes the following
predictions for the gravitational fields generated
by the gravitophoton force.
• In the first case, the gravitophoton force produces
a gravitational force above the disk in the zdirection
upward and also in the radial direction.
• In the second case, the gravitophoton force is in
the azimuthal direction only (experiment by Tajmar
et al.).
It is well known that a rotating superconductor generates
a magnetic induction field, the so called London moment
B=−
2me
e
¤ (3)
where ω is the angular velocity of the rotating ring and e
denotes elementary charge. It should be noted that the
magnetic field in Tajmar's experiment is produced by the
rotation of the ring, and not by a current of Cooper pairs
that are moving within the ring. This is a major difference
between the experiment of Fig. 3 and the proposed experiment
depicted in Fig. 4. Therefore the velocity of the
Cooper pairs with regard to the lab system is given by rω
in the experiment of Fig. 3 while the maximal velocity of
Cooper pairs in Fig. 4 is given by the maximum energy
8
z
e¤z
e¤r
e¤¤
Figure 4: Rotating superconducting torus (Niobium) modified
from Tajmar et al. All dimensions are in mm. A cylindrical CS
(r, θ, z) with origin at the center of the ring is used. In Ring
accelerometers measured a gravitational acceleration of some
100 μg in the azimuthal (tangential, θ) direction when the ring
was subject to angular acceleration, ¤˙ . No acceleration
was measured in the z-direction (upward). If the direction of
rotation is reversed, the acceleration field changes sign, too.
gap, respectively its quantum mechanical counterpart.
The major difference between the two experiments lies in
the generation of the magnetic induction field B. Tajmar
and his colleagues simply postulate an equivalence between
the generated B field, Eq. (3) with a gravitational
field by proposing a so called gravitomagnetic London effect.
However, this transformation between electromagnetics
and gravitation is introduced ad hoc and contradicts
current physics, since the four known physical forces
do not allow such a direct coupling.
On the other hand, this kind of coupling is a basic fact of
EHT, because of its six fundamental interactions, which
foresee such a conversion of hermetry form H7, describing
photons, into the hermetry form H5, describing the
gravitophoton interaction.
Let R denote the radius of the rotating ring, then Eq. 3
puts a limit on the maximal allowable magnetic induction,
Bmax, which is given by
Bmax
2 =14
me
e2
k BT C
R2 . (4)
If the magnetic induction exceeds this value, the kinetic
energy of the Cooper pairs exceeds the maximum energy
gap, and the Cooper pairs are destroyed. The rotating ring
is no longer a superconductor. Moreover, the magnetic induction
must not exceed the critical value BC(T), which is
the maximal magnetic induction that can be sustained at
temperature T, and is dependent on the material. EHT predicts
that the magnetic induction field B is equivalent to a
gravitophoton (gravitational) field bgp . Therefore, the following
relation holds, provided that B is smaller than Bmax
bgp∝ B
Bmax
B (5)
As soon as B exceeds Bmax the gravitophoton field vanishes.
From EHT the following general relationship between
a magnetic and the neutral gravitophoton field, bgp, can be
derived
bgp=¤ 1
¤1−k ¤¤1−ka¤
−1¤ em
e
B
Bmax
B (6)
where k = 1/24 and a = 1/8. The dimension of bgp of is s-1.
Inserting Eq. 3 into Eq. 6, using Eq. 5, and differentiating
with respect to time, results in
∂bgp
∂ t
=¤ 1
¤1−k ¤¤1−ka¤
−1¤ 2e
me
B
Bmax
∂ B
∂t
. (7)
Integrating over an arbitrary area A yields
∫∂ bgp
∂t
⋅d A=∮g gp⋅d s (8)
where it was assumed that the gravitophoton field, since it
is a gravitational field, can be separated according to Eqs.
(1, 2). Since the above formulas will be applied to the experimental
configurations depicted in Figs. 3 and 4, cylindrical
coordinates r, θ, z are employed. ggp is the acceleration
field generated by the gravitophoton field. Combining
Eqs. 7 and 8 gives the following relationship
∮ ggp⋅d s=¤ 1
¤1−k ¤¤1−ka¤
−1¤ 2e
me
∫ B
Bmax
∂ B
∂t
⋅d A (9)
From Eq. 3 one obtains
∂ B
∂t
=−
2me
e ¤˙ (10)
Next, we apply Eqs. 9 and 10 to the experimental configuration
of Fig. 3, calculating the gravitophoton acceleration
for the in-ring accelerometer. It is assumed that the
accelerometer is located at distance r from the origin of
the coordinate system. From Eq. 3 it can be directly seen
that the magnetic induction has a z-component only. From
Eq. 9 it is obvious that the gravitophoton acceleration is
in the r-θ plane. Because of symmetry reasons the gravitophoton
acceleration is independent on the azimuthal angle
θ, and thus only has a component in the circumferential
(tangential) direction, denoted by e¤¤ . Since the gravitophoton
acceleration is constant along a circle with radius
r, integration is over the area A=¤r2 e¤z . Inserting
Eq. 10 into Eq. 9, and carrying out the integration the following
expression for the gravitophoton acceleration is
obtained
ggp=− 1
10
B
Bmax
¤˙ r (11)
where the minus sign indicates an acceleration opposite to
the original one and it was assumed that the B field is homogeneous
over the integration area. Now the experimental
values taken from the paper by Tajmar et al. will be inserted.
The following values are used:
¤˙ =103rad /s2 ,r=3.6×10−2m ,B/ Bmax=3.97×10−4
where the angular acceleration was determined from the
slope fit of Fig. 6 in ref. [15] and the r value was determined
from Fig. 4 (R = 36 mm). The ratio of the magnetic
fields was calculated from the following formula, obtained
by dividing Eq. 3 by the square root of Eq. 4
B
Bmax
= 1
¤7 ¤ me
k BT C ¤1/ 2
¤R. (12)
Inserting an estimated average value of ω = 175 rad/s,
me = 9×10-31 kg, kB=1.38×10-23 J/K, TC = 9.4 K, and
R = 7.2×10-2 m, this ratio is calculated as 3.97×10-4. From
Fig. 6 in ref. [15] an experimental value of about 1.0×10-4
9
g was determined. Inserting the proper values into Eq. 11
finally delivers the theoretical value of the gravitophoton
acceleration for the experiment by Tajmar et al.
ggp=1.3×10−4 g . (13)
Compared to the theoretical value of Eq. 13 there is a
close agreement between the predicted gravitophoton
force and the measured acceleration. It should be kept in
mind that the exact angular velocity was not known and
an average value of 175 rad/s was used. Considering both
the mathematical and physical complexity of the derivation
the closeness of theory and experiment is remarkable.
The results might need to be adjusted for the exact experimental
values. It should be noted that values of k and a
have been derived some ten years ago and are published
in [22]. No parameter was adjusted in the derivation of
Eq. 11. Moreover, the theory also correctly predicts direction
and sign of the acceleration field. This is seen as a
sign that the predicted six fundamental interactions may
exist in Nature.
4.1.3 Space Device Based on Field Propulsion
The experiment by Tajmar et al. generates an azimuthal
gravitational field, and thus is not suitable for propulsion.
The lesson learned from the experiment by Tajmar et al.
is the fact that the coupling to bosons (Cooper pairs) is of
prime importance. However, employing the general
Heim-Lorentz force equations to the experimental setup
of Fig. 3, Heim-Lorentz force now produces force components
in the radial r and z- directions. These components
are given by
Fr e¤r=
vC
c
me ¤v¤
T bz e¤¤×e¤z ¤ (14)
F z e¤z=
vC
c
v¤
T
c
mn v¤
T bz ¤e¤¤×e¤z ¤×e¤¤
(15)
where vC is the velocity of the Cooper pairs in the superconducting
solenoid (Fig. 3), v¤
T=10m/ s denotes the
velocity of the rotating disk or ring, and bz is the component
of the (gravitational) gravitophoton field bgp (dimension
1/s) in the z-direction. In contrast to the fermion coupling,
experimental requirements are modest. The following
assumptions were made: N=100 number of turns of
the solenoid, current of some 1-2 A (needed to calculate
bz), diameter of solenoid 0.1 m. A detailed analysis predicts
an acceleration in z-direction of some 6.0×10-5 g.
From these numbers it is clear that, if theoretical predictions
are correct, the realization of a workable space propulsion
device that can lift itself from the surface of the
Earth seems to be feasible.
Conclusions and Future Work
In this paper an overview of the current status of space
propulsion was given. It has been shown that even with
an advanced fission propulsion system, space travel will
be both very limited and very costly. Travel time to other
planets will remain high. Metric engineering of spacetime
or using wormholes does not seem to be technically feasible.
On the other hand, the recent experiment by Tajmar,
if confirmed, has shown that a coupling between electromagnetism
and gravitation exists, which allows the generation
of artificial gravitational fields. EHT, which uses an
internal 8-dimensional space, has predicted this kind of
coupling and foresees six fundamental physical interactions.
The theory was successfully applied to predict the
outcome of Tajmar's experiment and also provides guidelines
for an experimental setup that can be used as field
propulsion device. Research therefore should focus on the
refinement of the experiment as well as on the theoretical
foundation of EHT.
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