Future Space Propulsion Based on Heim's Field Theory
12/05/2014 22:35
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Acknowledgments
The authors are grateful to Prof. Dr. Dr. A. Resch,
Director of the Institute of Grenzgebiete der
Wissenschaften, Leopold-Franzens Univ.
Innsbruck, Austria for providing access to Heim's
legacy and his hospitality.
The authors are grateful to Prof. Dr. T. Waldeer
for numerous discussions, and T. Gollnick and O.
Rybatzki, Univ. of Applied Sciences, Salzgitter,
Germany for producing some of the figures.
This research was partly funded by the ministry of
Science and Culture of the State of Lower Saxony,
Germany.
Now is the time to take longer strides
time for a great new American enterprise
time for this nation to take a clearly leading role in
space achievement,
which in many ways may hold the key to our future
on earth1
President Kennedy's message to the
congress on May 25, 1961
1It does not seem that the old Europe currently has any vision of
space
Presenttattiion Overviiew
Space Viisiionariies and Space Transporttattiion
Physiicall Ideas off Heiim''s Uniiffiied Fiielld Theory
Cosmogony off Space and Matttter
Graviittophotton Force ffor Space Propullsiion
Experiimenttall Settup ffor Graviittophotton Force
Intterpllanettary and Inttersttellllar Miissiions
Concllusiions and Futture Work
NASA''s Breaktthrough Physiics
Propullsiion Program Goalls
no ffuell,,
superrllumiinall speed,, and
no excessiive amountts off enerrgy
needed ffor a revolluttiionary space
propullsiion systtem
miightt be mett by
Heiim''s Uniiffiied Fiielld Theory
by Marc G. Millis et al., NASA Glenn Research Center
Space Viisiionariies and
Space Transporttattiion
Space Transportation Originator
von Braun's Vision of Space Flight
Space Transportation Revolutionary?
Space Transportation Breakthrough
Physiicall Ideas off Heiim''s
Uniiffiied Fiielld Theory
From the Mathematical to the Physical World
Physical World
discrete space time
Mathematical
world
nondimensional
concepts
Number theory
Ideal
Heim:
1. From dimensionless constants of the mathematical world to
the physical world.
2. From the diameter of the primeval universe, all physical constants
can be derived.
ℏ , e ,¤ ,¤
Real
Classical Relativity
Theory
Theory of
elementary Particles
continuous space time discrete space time
extending the structure
of classical relativity ¤
¤(metron)
ℝ
4 ℝ
8
Elementary particles are elementary in the sense that they
cannot be decomposed into subcomponents. However, simple
elementary particles are comprised of volumes in , built from
a set of 2D metrons. These particles, however, possess structure
visible as different zones from scattering experiments.
ℝ
8
Galilean
physics
Quantum
mechanics
Special
Relativity
Newtonian
Gravitation
General
Relativity
Quantum
field
theory
Heim:
Eigenvalue equation
for elementary
particles
Heim:
Modified
Newtonian
Law
2 new forces coupling
between electromagnetism
and gravitation
c = vacuum speed of light
v = velocity of ponderable
mass (rest mass )
= metron
m', c', v': quantities after inertial
transformation
Heim space : discrete, metrons
Riemann space: continuous
≠0
G
v¤∞
ℏ
G
ℏ
v¤c
G
Riemann
ℏ
v¤c
¤
ℏ
v '¤v
c '¤c
Heim
ℝ
3
ℝ
4
ℝ
8
ℝ
8
ℝ
4
¤
¤
Heim Space 8-Dimensions
Discrete spacetime, Metron ¤
Inertial Transformation
m' < m
c' > c
v' > v
Physiicall Coordiinattes iin
8D Heiim Space
The metric tensor in 8-space comprises several subtensors, such that each
subtensor is responsible for a different physical interaction. In the same way the
metric tensor of Einstein's GRT acts as a tensor potential for gravitation, the
additional subtensors constructed from the quantized Heim space, , are
responsible for all physical interactions in our universe. In other words, the
subspaces in in which the individual metric tensors are specified, are the
cause of physical forces. In that respect, we can speak of a completely
geometrized theory. In Heim space four groups of coordinates are discerned:
1. ℝ3, spatial coordinates (real) (ξ1
,
ξ
2, ξ3),
2. T1, time coordinate (imaginary) (ξ4),
3. S2, entelechial and aeonic coordinates (imaginary) (ξ5,
ξ6),
4. I2, information coordinates (imaginary) (ξ7,
ξ8).
ℝ
8
ℝ
8
ℝ
8
Physiicall Coordiinattes iin
8D Heiim Space
gi k=
∂ xm
∂¤¤
∂¤¤
∂¤i
∂ xm
∂¤¤
∂¤¤
∂¤k
x
m¤¤¤¤¤i¤¤ ,
where indices α, β = 1,...,8 and i, m, k = 1,...,4.
For a metric subtensor to represent a physical interaction, it must contain
coordinates of subspaces S2 or I2, the so called trans-coordinates.
Inerttiiall Transfformattiion iin Heiim''s Theory
P=m0 ¤1−v2/ c2¤−1/ 2¤v , ic¤
=¤mv , imc¤=¤ p , imc¤
mv=m' v '
p=mv
Since the magnitude of P is an invariant, both momentum and energy
conservation hold:
mc=m' c'
with
and
Since m> m' , it follows that c' > c and v' > v and therefore v'/ c' = v / c.
Inerttiiall Transfformattiion iin Heiim''s Theory
Owing to the invariance of the Lorentz matrix with respect to an inertial
transformation, which is rooted in the fact that v'/c' = v/c, superluminal
velocities should be possible. There is no contradiction to special relativity,
since an inertial transformation is not considered in SRT. The argument in
SRT is, that if v > c, then β = v/c becomes imaginary. Thus, it is concluded
that no observer can possess a velocity greater than that of light relative to
any other observer. In an inertial transformation, however, β remains
positive.
Such a transformation is not possible in SRT or GRT, since it is a
consequence of the unification of physical interactions and the polymetric
in Heim space ℝ8.
Cosmogony off Space and Matttter
The Quanttiized Bang
The primeval universe came into existence when the size of a single
Metron covered the surface of the universe
The primeval universe expanded and the Metron size was reduced, while the
number of Metrons increased
Most of the time the primeval universe was without matter
Cosmiic Numberrs
¤~D
−6/11
ℏ~D
−8/11
and G~D
−13/11
¤0~D
13/11
and ¤0~D
−3/ 11
iin Heiim''s uniiverrse,, allll physiicall consttantts depend on a
siinglle llengtth scalle
D = 10125 m current diameter of primeval
τ = 10-70 m2 current Metron size,i.e.,
quantized elemental surface area
alternatively, all constants may be
expressed through τ instead of D
Heiim''s Modiiffiied
Newttoniian Law off Grraviittattiion
grraviittattiionall attttrracttiion iis 0 att diisttances smallllerr tthan tthe Schwarrzschiilld rradiius,,
grraviiattattiionall attttrracttiion goes tto 0 att diisttances off some 46 Mpc,,
grraviittattiionall attttrracttiion becomes rrepullsiive att diisttances llarrgerr tthan 46 Mpc and
goes agaiin tto 0 att tthe Hubblle rradiius,,
Accorrdiing tto Heiim ((tthe derriivattiion off tthe fforrmulla bellow was nott callcullatted
iindependenttlly by tthe autthorrs)),, Newtton''s llaw needs tto be modiiffiied fforr llarrge
diisttances by a negattiive tterrm and tthus becomes rrepullsiive::
a=G
m¤r ¤
r 2 ¤1−
r 2
¤2 ¤ , ¤=
h2
Gm0
3
m
0
being the mass of a single nucleon comprising the mass of the field source.
Mass m(r) is the total mass and comprises the ponderable and the field mass. The
formula above is an approximation only.
Heim's modified law
Newton's law of gravitation F
¤ R
H
r¤∞
F~
1
r
2
F~
1
r
2
1−
r
2
¤
2
Gravitation goes to 0 at approximately 46 MParsec
0
0 R
S
R
S
¤ ~ 46MPc
R
H
~
(Schwarzschild radius)
Hubble radius
10
115
s 10
15
s
10
100
0 0
Decay of the Maximon
particle,
inflationary phase
Quantized Bang
Generation of
matter, length
scale at Planck
length
Time scale for the Universe (seconds)
8D discrete spacetime
Heim
Physical
universe
Many physical universes
embedded in the primeval
universe
Primeval universe:
geometric structure
only, no matter
Physical universe:
existence of matter
primeval universe
(Trinity of spheres)
physical
universe
decreasing length scale
constant length scale,
constant physical quantities
Graviittophotton Force ffor
Space Propullsiion
sieve operator
Photon Gravitophoton
Inertial Transformation to reduce
the inertial Mass of a Body
Since m'< m conservation of energy and momentum
requires that
c '¤c , v'¤v
This implies that Lorentz matrix remains unchanged
1−
v
2
c
2
= 1−
v '
2
c '
2
Heiim--Lorrenttz Equattiion
The gravitophoton force is surprisingly similar to the electromagnetic
Lorentz force.
It was termed the Heim-Lorentz force by these authors.
This equation is the basis for the following gedanken-experiment.
m is the mass of the rotating ring, v
T its velocity, and H is the magnetic
field generated by the current loop. It should be noted that the sign of
depends on the direction of the velocity of the rotating body. As a rule,
the velocity of the charges in the current loop and the circumferential
velocity of the rotating ring must be in opposite directions.
F
gp=¤p
e ¤0
vT×H
¤
p
=
32
3 ¤ Nw
gpe
w
ph ¤2
¤Nw
gpa¤4¤ ℏ
m
p
c ¤2
d
d
0
3
Z
Gravitophoton Force
Experiimenttall Settup ffor
Graviittophotton Force
¤¤
¤
¤
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Gravitophoton Force in Neutron Stars (Pulsars)
Intterpllanettary and
Inttersttellllar Miissiions
Mission to Mars
Speed
Travel time ~ 4 days
1.5×10
6
m/ s
Miissiion tto a Pllanett 100 Ly ffrrom Earrtth
The interstellar mission to a planet some 100 ly away from earth would take place in two
stages.
In stage one, lasting 30 days, the spacecraft reaches a speed of some 0.1c, using
gravitophoton acceleration.
In stage two, the inertial mass of the spacecraft is reduced by a factor of 10-4.
Because the ratio of the initial and the reduced inertial masses is proportional to the ratio
of the final and initial velocities of the spacecraft, which follows directly from the
conservation of momentum and energy), the final speed of the spacecraft is 10 3 c.
The spacecraft would travel in some kind of hyperspace in which the speed of light
c' = 104 c.
The total travel time would be 0.1 y + 2×30 d, which is approximately 3 months. A
return trip would be feasible in 6 months time. A major advantage would be that
during 4 months, the astronauts are subjected to an acceleration of 1 g.
Conclusions
Heim's theory is an extension of Einstein's theory in that each physical interaction and its
associated interaction particle is described in a quantized higher dimensional space. In other
words, all forces and all material particles are of geometric origin.
Elementary particles possess a complex dynamic structure that also exhibits zones within such
a structure. In the 8-dimensional space, termed Heim space by the authors, several metric
subtensors can be formed. Each of these subtensors, called a Hermetry form, is responsible of
a physical interaction or interaction particle.
When these metric subtensors are formed, two new additional interactions along with their
interacting particles occur. One of these particles, termed the gravitophoton, is responsible for
the reduction of the inertial mass of a material body (spacecraft).
This physical effect would lead to an inertial transformation in the Lorentz matrix, that, in
principle, allows for superluminal travel, because of the conservation of momentum and
energy. The kinetic energy of the spacecraft, flying at a velocity greater than the vacuum speed
of light, has not increased, since its inertial mass decreased. Otherwise, any spacecraft, flying at
velocities close to c, would need an amount of kinetic energy that is impossible to supply and to
pay for.
In that respect, the goals of NASA's Breakthrough Physics Propulsion Program, namely, no
fuel, superluminal speed, and no excessive amounts of energy needed for a revolutionary space
propulsion system can be met, provided, of course, that Heim's theory represents physical
reality.
Future Work
Future work will focus on a more precise prediction of the
gravitophoton field with emphasis on the experiment suggested in
order to measure the reduction of inertial mass. Computations will
be refined to give a better prediction of the performance of the
proposed propulsion device. Furthermore, the physical model
underlying this propulsion system will be given a more extensive
description.
