WARP DRIVE AND GRAVITY CONTROL FOR PROPULSION NEW THEORETICAL RESULTS GO FIRST SUCCESSFUL WARP DRIVE FLIGHT  GO ROTATION SPEED OF THE MILKY WAY GALAXY GO UNIFYING GENERAL RELATIVITY AND QUANTUM MECHANICS: NEW RESEARCH GO NASA CONCEPT OF AN ARTIFICIAL GRAVITY (1G) SPACESHIP GO GENERAL RELATIVITY THEORY AND APPLICATIONS GO GRAVITATIONAL WARP DRIVE FOR SPACE TRAVEL GO EFFECTS OF DARK ENERGY ON COSMOLOGY GO GRAVITY AND CURVATURE OF SPACETIME GO TEST FOR FLATNESS OF SPACETIME GO HOW TO DETERMINE, E = MC2 GO SPACETIME CURVATURE GO | MAIN PAGE | SOFTWARE LIST | AEROTESTING | MISSION | RESUME | Copyright © 1999-2021 John Cipolla/AeroRocket. All rights reserved

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 Alcubierre warp 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 rs(t) = [(x-xs(t))2 + y2 + z2]1/2. Figure-7 represents the metric-shape function, f(rs) 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 This Relativistic Warp 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 by the 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) Back to TOP

Warp Drive Propulsion Using
Magnetic Fields To Distort Space-Time

OR

First Successful Warp Drive Flight
By John Cipolla, Copyright August 14, 2020

Page 1 of 11
This full paper may or may not be released in the future

Figure-1, Alcubierre relativistic warp bubble

    
         Figure-2a, Magnetic field warp bubble                       Figure-2b, Space-time expansion behind m

Figure-3, Magnetic field projectile position at apogee

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RELATIONSHIP BETWEEN QUANTUM MECHANICS AND RELATIVITY FOR A THEORY OF EVERYTHING Read more about this breakthrough research OR Download John Cipolla's research paper "Demonstrating the Relationship Between Quantum Mechanics and Relativity", 2019, viXra e-print archive (4.5 MB) By John Cipolla BACK TO TOP

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) BACK TO TOP 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. BACK TO TOP 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, F when 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 VH = H*(t/t0)*d, where t0 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 = mc² 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, s² 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
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