This analysis
provides insight into how magnetic fields may be
combined to produce a warp bubble like the
expansion-compression warp bubble predicted by
Alcubierre’s solution derived from Einstein’s theory of
general relativity but without the requirement for
negative energy. The shape of the magnetic field warp
bubble generated by this analysis indicates a subluminal
(v < c) type of warp drive propulsion based on magnetic
fields may be technically possible. These results are based
on the theory that magnetic field forces of attraction and
repulsion are a relativistic effect caused by fast moving
electrically charged particles that distort space-time.
Where, magnetic field forces of attraction and repulsion are
a relativistic effect because space-time length contraction
in the direction of moving electrons increases the density
of charged particles and associated electrical forces. The
expansion of space-time and the simultaneous
compression of space-time in regions around intense
magnetic fields described here are similar in principle to
Alcubierre’s superluminal (faster than light) warp drive.
This newly defined and simplified mechanism is in fact a
true warp drive. Where, it is postulated that objects whose
inertia has been reduced by a magnetic field warp
bubble can accelerate to speeds and altitudes greater than
similar objects of equivalent mass. As discussed in
Introducing Physical Warp Drives the magnetic field
warp bubble proposed in this paper only requires standard
methods of propulsion to accelerate. Finally, an
experimental device based on the magnetic field warp bubble
successfully accelerated a projectile to altitude and speed
greater than objects of equivalent mass when accelerated by
magnetic-pole to magnetic-pole field orientation.
Nomenclature
B m0 m0 i d Xk Yj nturns
=Magnetic field
potential
=Magnetic monopole charge
=Permittivity of free space
=Current flowing through conductor =Distance between charges
=X free field
locations
=Y free field
locations
=Number of coil turns
Figure-1, Alcubierre warp field
Figure-2, Magnetic field warp bubble
Figure-3, Space-time
expansion-compression around m
Figure-4, Energy field surrounding UFO captured in
flight, v < c
Figure-5, Magnetic warp field projectile position
at apogee
Figure-2: Warp bubble geometry illustrating
how spacetime compression and expansion
propel a warp bubble and an enclosed starship through space to
distant stars
ALCUBIERRE WARP METRIC RESULTS (10/15/2008)
Figure-3, Figure-4 and Figure-5: Theoretical Alcubierrewarp metric derivation using MathCAD
MathCAD results for the
Relativistic analysis of the Alcubierre
faster than light
warp metric is illustrated in the above contour plots. Figure-3 represents a light cone
where rs(t) = [(x-xs(t))2 + y2
+ z2]1/2. Figure-4 represents the metric-shape function, f(rs) also called the "top hat"
function. Figure-5 displays the resulting warp
metric for faster than light space travel. The complete MathCAD
analysis to determine the relativistic warp metric for faster than light star
travel is presented below.
Figure-6, Hypothetical flight to a star 4.3 light years away
referenced in The Warp Drive: Hyper-fast Travel Within General
Relativity
GENERAL RELATIVITY AND WARP DRIVE THEORY ThisRelativisticWarp drive theory uses the
concept of a warp bubble to avoid violating the
universal speed limitation which is the speed of light, c.
Basic to the study of General Relativity is the concept of spacetime curvature embodied bythe following
statement, "Matter-energy tells spacetime how to curve and spacetime tells
matter-energy how to move". The concept of spacetime curvature
is summarized in the Einstein equation which is a result of
the theory of General Relativity. According
to the Einstein equation, matter and energy tell spacetime
how to curve and in turn spacetime tells matter and energy
how to move. Where, matter and energy are defined by the
stress-energy tensor (T) and spacetime curvature is defined
by the Riemann curvature tensor (R). In summation, the
Einstein equation relates spacetime curvature and
accelerated motion of a matter-energy system and the
implication that accelerated motion and the effects of
gravity are not distinguishable. Hence, artificial gravity
can be created by simply rotating a spacecraft to create the
effect of gravity on long journeys into space and a warp
bubble can be used to travel to distant places at many times
the speed of light without locally exceeding the speed of light
in the warp bubble.
WARP BUBBLE PHYSICS
According to General Relativity gravity and acceleration are not
distinguishable and are caused by the curvature or warp metric of
spacetime.
A warp bubble is a specific warp metric solution of General
Relativity and is a combination of positive and negative energy
fields that pushes and pulls our starship forward to bring our
destination to us just like a conveyer belt. The exotic ingredient required to make a warp
bubble is negative energy which has the unusual property of
being able to make ordinary matter fall up in a gravitational
field. According to General
Relativity the spacetime in front of a warp bubble is
compressed pulling our destination to us. At the same time the spacetime behind a warp bubble is expanding pushing us to our
destination. The compression and expansion process happens in an instant and at many times
the speed of light making faster than light travel possible. The
combination of positive and negative energy produces an
expansion of space behind the bubble and a contraction of space
in front of the bubble. in other words, creating space behind the bubble pushes us to our destination
and destroying space in front of the bubble pulls us to our destination.
This mechanism allows us to travel many times faster than the
speed of light (see Starship Warp Velocity) relative to the
Earth without exceeding the speed of light in our local frame of
reference, the warp bubble. The warp bubble itself is made of fields of positive energy at
either end and a band of negative energy around the middle.
These energy fields create huge gravitational effects so powerful the
warp bubble can distort spacetime without having to accelerate
the traveler to achieve faster than light velocity. The main requirement,
negative energy also called vacuum energy is a property of a vacuum where subatomic
particles smaller than an atom dart into and out of existence
almost instantaneously. According to the rules of quantum mechanics
negative energy creates a negative quantum pressure that
propels the warp bubble and therefore our starship forward. An
interesting observation is that we may already see the effects
of negative energy because astronomers have observed that our
universe is expanding due to the presence of dark energy. It is
theorized that dark energy fills the vacuum of space between the
galaxies and is the cause for the expansion and increasing
acceleration of the universe.
Therefore, dark energy and negative energy are probably the same
"stuff" required to make a warp bubble possible.
General Relativity states the equivalent mass-energy of a planet
the size of Jupiter is required to create a warp bubble. Because
producing negative energy is beyond our capability the objective
of this research is to find an alternate way to create a
relativistic warp bubble without the need for exotic matter or negative
energy.
REFERENCES FOR
GENERAL RELATIVITY
Gravitation, Charles W. Misner, Kip S. Thorne and John
A. Wheeler SPACETIME and GEOMETRY An Introduction to General
Relativity, Sean M. Carroll Relativity Demystified, David McMahon
WARP DRIVE
REFERENCES
The
Warp Drive: Hyper-fast Travel Within General Relativity,
Miguel Alcubierre
LIGHT RAYS BEND
AROUND MASSIVE OBJECTS TOP
The curvature of space time causes the path of a light ray
to bend in the region around a massive object. A ray of
light as it approaches the gravitational charge of a massive
object undergoes a deflection through the angle,
Fwhen the separation distance, D
is small enough. Using the Schwarzschild metric
solution given by the principle of equivalence the equation
for the deflection angle, F
of a ray of light is illustrated in Figure-3.
Several observations for the deflection of light by the Sun
during solar eclipses are in agreement with this simple
light ray deflection equation.
Figure-1, Deflection of light determined by the Schwarzschild
metric
GENERATING
GRAVITY WAVESTOP
It is well known and documented in GRAVITATION and
other books about general relativity that rotating systems
like binary stars, black holes and all rotating massive
objects generate gravitational waves due to the reduced
quadrupole moment of the rotating disturbance. Figure-1
illustrates how a massive rotating system analogous to a
binary star generate gravitational disturbances in spacetime.
Gravity waves are generated by a rotating mass-energy system
because the differential arrival time from opposite sides of
the system cause a phase angle between gravitational
vectors. Gravitational vectors from opposite sides of a
rotating system that initially oppose each other when the
system is stationary are drawn inclined at phase angle, dq
during rotation. The amplitude of the resulting
gravitational wave generates a reduced quadrupole moment
that when squared is proportional to the generated
gravitational power. Further, it can be shown that like
electromagnetic waves, gravitational waves have energy, U
that delivers momentum, p to a point in spacetime causing a
small net force, F to act at that point. The force, F is the
net gravitational wave force this research is attempting to
generate, enhance and measure.
Figure-4 presents a simple gravitational-wave analysis of a
binary star. This example is similar to the example
displayed in GRAVITATION on pages 979 and 980 where
the gravitational-wave power output of a massive rotating
beam is computed when the beam rotation frequency is
determined by balancing centrifugal force and beam material
tensile strength. The power radiated in the form of
gravitational waves by the rotating beam is only 2.27E-22
ergs/sec and the force imparted to an area 500 meters
away is only 1.89E-42 newtons. However, if the mass
or the rotation rate of the beam are greatly increased
possibly to speeds approaching the speed of light then a
form of gravity propulsion may be possible. In ways similar
to Alcubierre's warp metric, gravity waves produce repeated
regions of compressed spacetime followed immediately by
regions of expanded spacetime.
WHAT RADIATES GRAVITATIONAL WAVES: In applying the
equations that appear in Figure-2, Figure-3 and Figure-4 one must be
careful to ignore internal power flows that cannot radiate
gravitationally, that is internal motions that do not
accompany a time changing quadrupole moment. For example, a
normal star does not radiate gravitational waves because the
internal power flows associated with spherical pulsation and
axially symmetric rotation are not unbalanced motions.
However, dynamic astrophysical systems that do radiate
gravitational waves include stars that pulsate and rotate
wildly, collapsing stars, exploding stars, feeding black
holes and chaotic systems of stars.
GRAVITY WAVE PROPULSION - HYPOTHESIS: The power
output by a laboratory sized gravitational-wave generator is
very small unless the rate of rotation or the mass of the
beam is greatly increased. However, it is hypothesized
that if the ordinary mass-energy of a rotating beam
is increased to that of the planet Jupiter and if the rate
of rotation is kept the same at 4.456 revolutions per second
it may be possible to impart a force of 28.5 Newtons to an
object 500 meters away. Please see Figure-5 for the basic
methodology required for carrying out this experiment.
Figure-1: Reduced quadrupole
moment generation of gravitational waves through spacetime.
Figure-2: Methodology to
approximate quadrupole gravitational-wave power
Figure-3: Order of magnitude
gravitational-wave power analysis
Figure-4: More precise method
to determine gravitational power radiated by a binary star
from GRAVITATION
Figure-5: Experiment for
generating gravity waves in the laboratory
EINSTEIN'S HYPOTENUSE AND E = mc2TOP
Einstein's hypotenuse is derived from Minkowski's flat
space-time metric, below.
The following light cone
plot displays space-time for S = 0.5, Xmax = 2 and c = 1.
Note that ct verses x (blue)
approaches the light cone (red)
as S approaches zero.
Figure-1,
Plot of the space-time interval, s2
verses
distance, x
in Minkowski space-time
REFERENCES FOR
GENERAL RELATIVITY
Gravitation, Charles W. Misner, Kip S. Thorne and John
A. Wheeler SPACETIME and GEOMETRY An Introduction to General
Relativity, Sean M. Carroll Relativity Demystified, David McMahon
_metric.gif)
According
to the Einstein equation, matter and energy tell spacetime
how to curve and in turn spacetime tells matter and energy
how to move. Where, matter and energy are defined by the
stress-energy tensor (T) and spacetime curvature is defined
by the Riemann curvature tensor (R). In summation, the
Einstein equation relates spacetime curvature and
accelerated motion of a matter-energy system and the
implication that accelerated motion and the effects of
gravity are not distinguishable. Hence, artificial gravity
can be created by simply rotating a spacecraft to create the
effect of gravity on long journeys into space and a warp
bubble can be used to travel to distant places at many times
the speed of light without locally exceeding the speed of light
in the warp bubble.
Relativity the spacetime in front of a warp bubble is
compressed pulling our destination to us. At the same time the spacetime behind a warp bubble is expanding pushing us to our
destination. The compression and expansion process happens in an instant and at many times
the speed of light making faster than light travel possible. The
combination of positive and negative energy produces an
expansion of space behind the bubble and a contraction of space
in front of the bubble. in other words, creating space behind the bubble pushes us to our destination
and destroying space in front of the bubble pulls us to our destination.
This mechanism allows us to travel many times faster than the
speed of light (see Starship Warp Velocity) relative to the
Earth without exceeding the speed of light in our local frame of
reference, the warp bubble.
The warp bubble itself is made of fields of positive energy at
either end and a band of negative energy around the middle.
These energy fields create huge gravitational effects so powerful the
warp bubble can distort spacetime without having to accelerate
the traveler to achieve faster than light velocity. The main requirement,
negative energy also called vacuum energy is a property of a vacuum where subatomic
particles smaller than an atom dart into and out of existence
almost instantaneously. According to the rules of quantum mechanics
negative energy creates a negative quantum pressure that
propels the warp bubble and therefore our starship forward. An
interesting observation is that we may already see the effects
of negative energy because astronomers have observed that our
universe is expanding due to the presence of dark energy. It is
theorized that dark energy fills the vacuum of space between the
galaxies and is the cause for the expansion and increasing
acceleration of the universe.
Therefore, dark energy and negative energy are probably the same
"stuff" required to make a warp bubble possible.
