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

Summary of Basic Supporting
Theory
1. Magnetic field forces of attraction and repulsion are
a relativistic effect caused by fast moving electrically charged
particles that curve space-time.
2. Powerful magnetic fields like all mass-energy, curve
space-time.
3. Space-time curvature is caused by the uneven
distribution of mass-energy.
4. The book GRAVITATION proves that gravity waves
including the warp bubble postulated here move through
space-time as gravitational quadrupole radiation.
5. The magnetic warp bubble described by Equation-3 and
displayed in Figure-5a and Figure-5b travel through space-time
as gravitational quadrupole radiation that expands and
compresses space-time into the form of a closed magnetic
bubble.
6. The postulated warp bubble moves through space-time as
a subluminal (v < c) disturbance.
7. Hypothesis and Experiment: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. An experiment that used 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.
This hypothesis was partially verified by a separate experiment
that used a “warp core” having approximately the same magnetic
field intensity to accelerate the same projectile using the
magnetic-pole to magnetic-pole method but without the presence
of the magnetic field warp bubble. These experiments are
continuing.

(1) WARP DRIVE FOR SPACE TRAVELTOP
John
Cipolla is performing unique research in the area of gravitational
warp drive
technology and gravity control for faster than light star travel. The
illustrations below show a spacecraft being accelerated
while enclosed within an artificially generated warp bubble.
The following results from
the theory of General Relativity illustrate how
a warp bubble uses opposing regions of expanding
and contracting spacetime for propelling a starship at velocities exceeding
the speed of light. This is a work in progress based on
a new method for warping spacetime to generate warp
bubble disturbances without the need for exotic matter
or negative energy. Experiments are being conducted to
evaluate the method's capability for generating the
theoretical warp metrics depicted in Figure-2, Figure-3, Figure-4
and Figure-5.

Spacecraft concepts that use
warp drive technology

Figure-1: Warp bubble traveling
adjacent to the Earth (not to scale)

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-6 represents a light cone
where r_{s}(t) = [(x-x_{s}(t))^{2} + y^{2}
+ z^{2}]^{1/2}. Figure-7 represents the metric-shape function, f(r_{s}) also called the "top hat"
function. Figure-8 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.

--- End Warp Drive Analysis ---

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. It is proposed that a replacement for negative energy
may be possible by using positive energy in unique ways to generate an energy signature
equivalent to the Alcubierre warp metric displayed in
Figure-11 of the RESULTS TO DATE
section.

SPECIAL REFERENCES:
Note-1: 2-D warp bubble from John
Cipolla's Warp Drive Notes, 1974.
Note-2: Negative energy composite view based on Sci Fi
Science, How to Explore the Universe: Where Dr Michio
Kaku reveals how we could one day build a warp drive.

Figure-9: MathCAD
warp bubble analysis of a hypothetical flight to a star 4.3 light years away

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 Warp Drive, When? (NASA)

ESTABLISHING THE ANALOGY
BETWEEN
GENERAL RELATIVITY AND POTENTIAL VORTEX FLOW
AND RUDIMENTARY WARP DRIVE PROPULSION
BY JOHN CIPOLLA (1990 to 2015)
NEW PAPERS AVAILABLE By John R. Cipolla,
Copyright 2015

Research has
shown that an analogy exists between potential vortex flow
and the generation of space-time curvature around massive
objects as predicted by Einstein’s theory of General
Relativity (GR). The analogy between GR and potential vortex
flow is based on results from potential vortex
experimentation, GP-B researcher statements, free-surface shape extracted from Schwarzschild’s metric, a
unit analysis of the curvature and energy-momentum
components of potential vortex flow and the analogous
components from Einstein’s Field Equations and black hole
dynamics compared to potential vortex dynamics. Predictions
based on this research
are made that indicate gravity control and rudimentary warp
drive is possible.

An implication for the existence of a superfluid potential vortex substratum is that interesting
fluid mechanical characteristics of space-time can be
revealed. Specifically, an interesting by product of a
superfluid substratum is the Magnus effect. The Magnus
effect is the force exerted on a rapidly spinning cylinder
or sphere moving through air or another fluid in a direction
at an angle to the axis of spin. The sideways force is
responsible for the swerving of balls when hit or thrown
with spin. For example, if an object composed of
energy-momentum rotates in the gravitational field of
another massive object a Magnus effect based on
the superfluid of space-time will impart a sideways force on
the object and an associated acceleration in the substratum.
In exactly the same way the surrounding fluid is deformed by
a spinning object, space-time will be compressed on one side
of the object and expanded on the other side of the object
generating an imbalance in space-time. The deformed
space-time surrounding the spinning object could be called a
warp bubble that uses the imbalance within space-time to
propel an object perpendicular to the field lines of the
surrounding superfluid. Speeds approaching the speed of
light are not practical but exotic materials are not
required for a device based on this technology. The
analogous Magnus effect in General Relativity that uses the
principals of fluid mechanics to model
space-time around a circular cylinder with circulation is
defined as a uniform flow plus a doublet plus a
vortex.

Rotating
mass-energy and resulting warped space-time (3)

Superfluid warp drive operating
in the Solar System (3)

Superfluid vortex
experiment (1, 2)

4-d space-time
interpreted by
GP-B as the surface of a
superfluid.
See
Gravity Probe-B (GP-B) for information

Related Publications by John Cipolla
“Potential Vortex
Transient Analysis and Experiment”, viXra
e-print archive, (2014)
"Hydrodynamic Analogue for Curved Space-Time and General
Relativity", viXra e-print
archive, (2014) "Rudimentary Warp
Drive Propulsion",
Warp-Drive.pdf,
(2015)
"Does Time Exist",
Does-Time-Exist.pdf, (2015)

TESTS TO BETTER UNDERSTAND GRAVITY
GRAVITATIONAL WAVES (8/9/2011)

Figure-16: Experiment to determine
magnetic force (F) verses
distance (r) separating a magnet from a small
cylindrical steel mass
and to prove magnetic forces obey the inverse square law
relationship.

Figure-17: Test results (red
dots) verses an inverse square law curve fit for magnetic
force verses distance.

Figure-18: Magnetic field analogy for a
gravity wave generator to determine distant particle motion.
Vector,
V illustrates the motion and velocity of a cylindrical steel mass
exposed to a rotating pair of magnets.
The steel mass is exposed to the quadrupole moment generated by the
rotating pair of ceramic magnets.
The mass follows an elliptical orbit that is perpendicular to the axis of
the rotating pair of magnets.

GRAVITATIONAL WAVES: The law of
gravitation is an inverse square law relationship as
are the laws relating the forces associated with monopole
static charges and dipole magnetism. In general the inverse
square law relates the intensity of a field effect to the
reciprocal of the square of the distance from the source of
the effect. The experiment illustrated in Figure-18 uses a
magnetic field analogy of a gravity wave generator to
demonstrate the effect quadrupole gravitational waves
have on spacetime and particle motion.

To demonstrate that dipole magnetic fields obey an inverse
square law relationship and therefore are a useful mechanism
to visualize quadrupole gravitational radiation for rotating
systems, Figure-16 demonstrates how force verses distance were
experimentally determined to generate the magnetic force
verses distance data presented in Figure-17. As expected
from field theory, dipole magnetism obeys the inverse square
law relationship. The following equation fits the force
verses distance data measured using the method illustrated
in Figure-16 where the relationship is F = C/r^2 and
C = 1.786E5 dyne*mm^2. Because dipole magnetism
obeys the inverse square law it can be assumed the experiment
illustrated in Figure-18 is a reasonable analogy for the
gravity wave generator presented in Figure-19 where several
masses possessing mass and energy are rotated at
high speed. During operation the cylindrical mass in Figure-18 follows a
highly elliptical orbit indicating the presence of an
external magnetic quadrupole field. Therefore, to understand
how gravitational quadrupole radiation affects particle
motion the rotating magnetic field experiment in Figure-18
is useful.

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-18 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-22 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-20 and Figure-21 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-21 for the
basic methodology required for carrying out this analysis.
However, achieving the mass-energy density for
successfully conducting this experiment does not yet exist
on the planet Earth. But, it is encouraging that negative
energy of the same density is not be required.

FURTHER INVESTIGATION: Using the reduced quadrupole
moment of rotating systems deserves further investigation.
For example, the theoretical warp bubble illustrated in
Figure-3 was created using frame dragging and
not negative energy as required by Alcubierre's
warp bubble. While the
theoretical warp bubble illustrated in Figure-3 looks
similar to the negative energy warp bubble illustrated in
Figure-1 and Figure-2 the frame dragging warp bubble needs
to be more clearly understood to determine its true
physical characteristics.

Figure-19: Reduced quadrupole moment
generation of gravitational waves through spacetime.

Figure-20: Methodology to approximate quadrupole
gravitational-wave power

Figure-21: Order of magnitude
gravitational-wave power analysis

Figure-22: More precise method to
determine gravitational power radiated by a binary star from
GRAVITATION

(2) GRAVITY AND CURVATURE OF SPACETIME
TOP
According to Einstein's
General Theory of Relativity gravitation is a
manifestation of the curvature of spacetime. Light and
particles of matter travel along geodesics while the geometry
in
which travel occurs takes place in spacetime not just
space. A geodesic is the shortest line between two
points that lies in a given surface. In curved space two
separate geodesics that start off parallel will
eventually cross or intersect. Because gravity is a
manifestation of geometry this behavior will occur in
the motion of particles on geodesics in spacetime. The
intersection of initially parallel geodesics is an
expression of gravitational tidal effects while
traveling within a gravitational field. For example, two
particles in free fall in a gravitational field will
initially move parallel to each other as they approach
the ground. However, because the particles are moving on
radial paths to the center of the massive object they
will seem to move toward each other if the distance
traveled is great enough. This is a description of the
tidal effects of gravity and the spacetime effect on
particles moving in spacetime. This phenomenon is also
called geodesic deviation.

Figure-2 represents the gravitational field determined
using the Schwarzschild metric solution for the
curvature of spacetime outside any spherically
symmetric mass like the Earth, Sun or a black hole. The
tidal effects of gravity on a volume of space as the
volume approaches a massive object is displayed. Changes
of space-extension or distortion of the volume is caused by the
curvature of spacetime.

Figure-1, Schwarzschild metric or line element for static,
spherically symmetric fields outside spherically
symmetric bodies. This equation describes the metric
structure of empty spacetime surrounding a massive body.

Figure-2, Volume entering the gravitational field of an object
modeled by the Schwarzschild solution

Furthermore,
the curvature of spacetime 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-3, Deflection of light determined by the Schwarzschild
metric

(3) TEST FOR FLATNESS
OF SPACETIME TOP
Sometimes it's necessary to
determine the degree to which spacetime is curved. The
following test for spacetime flatness is useful to
determine if the influence of a nearby massive object can be
ignored when trying to determine the relative position of
two particles or two space ships in orbit. The following example
is from page 30 of Gravitation by Misner and Thorne.

Statement of the Problem: A region just above the
surface of the Earth, 100 m x 100 m x 100 m (space
extension) is followed for 10^6 m of light-travel time (T ~
3 seconds). Using the Riemann curvature tensor determine the
uncertainty of measurement for the volume as it traverses
the space around Earth.

Figure-4, Example from Gravitation, page 30

(4) SPACETIME
CURVATURE TOP
The following is a general
method or procedure to determine the non-relativistic
change in the space extension of a volume, region or object
in the vicinity of a massive object caused by tidal effects
of gravity and spacetime curvature. This example is useful
to determine the dimensions of an object as it approaches a
black hole or to determine when spacetime can be considered
Euclidian (flat) or non-Euclidian.

Figure-5, Simple application of the Riemann curvature tensor

(5) GENERAL RELATIVITY THEORY AND APPLICATIONS TOP
The following series of simple
analyses are applications of General Relativity to
the study of Cosmology. Gravity dominates on large scales
making it possible to neglect nuclear and electromagnetic
forces for cosmological approximations. In addition, the
universe is to a very high degree "homogeneous" (the same at
every point) and "isotropic" (the same in every direction) making the spacetime metric nearly the same from one
point to another over large distances. For more information
please see the references especially
Relativity Demystified.

Figure-6, General Relativity theory and applications

6) EFFECTS OF DARK ENERGY ON COSMOLOGY TOP
The cosmology presented here is based on the
concept of dark energy and the resulting negative
pressure required for an expanding universe. These
concepts are important because designing a warp drive
depends on dark energy or something similar to generate
the signature warp bubble required for faster than light
star
travel.

The following are plots of the scale factor (a), Hubble
parameter (H), energy density (r)
and expansion velocity (VH/c) of the universe as a function
of time from the Cosmic Microwave Background which occurred 380,000 years after the
Big Bang. Generating these Cosmology results require the
following equations from Sean M. Carroll's text book, SPACETIME and GEOMETRY
an Introduction to General
Relativity. The equations required for this analysis are: Scale
factor (a), equation 8.183 on page 367, Hubble parameter
(H), equation 8.184 on page 367 and average mass density (r) of the
universe, equation 8.67 on page 336. Equation 8.67 is the Friedmann equation
which relates spacetime curvature (K), mass density and the expansion rate
(H) of the universe. Using the Friedmann equation average mass
density of the universe is determined by substituting K = 0 because the universe is observationally flat
over great distances. Finally, the expansion velocity of the universe is
V_{H} = H*(t/t_{0})*d,
where t_{0} is the present time from the CMB and d
is our present distance from the CMB. The CMB
is defined as the Cosmic Microwave Background which occurred
380,000 years after the Big Bang.

Figure-7, Results for scale factor, Hubble
parameter, energy density and expansion velocity of the
universe as
a function of time from when the Cosmic
Microwave Background (CMB) occurred 380,000 years after the
Big Bang

EINSTEIN'S HYPOTENUSE AND E = mc^{2}TOP
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-13,
Plot of the space-time interval, s^{2}
verses
distance, x
in Minkowski space-time

NASA CONCEPT OF AN ARTIFICIAL GRAVITY (1G) SPACESHIP
TOP

Figure-13, NASA concept for using artificial-gravity (AG) for
Mars exploration. R = 56m and 4 rpm.

Figure-14, Rotation radius of 56 meters and rotation rate of
4 rpm generates 1.0 g artificial gravity.

Figure-15, Free-body diagram illustrating how rotation
radius and rotation rate create gravity.
This concept illustrates equivalence between gravity
and normal acceleration.

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 Back to TOP