(1) GRAVITATIONAL WARP DRIVE FOR SPACE TRAVEL
John Cipolla is performing ground breaking 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 and Figure-4.

MathCAD results for the Relativistic analysis of the Alcubierre faster than light warp metric is illustrated in the above contour plots. Figure-5 represents a light cone where r_s(t) = [(x-x_s(t))² + y² + z²]^1/2. Figure-6 represents the metric-shape function, f(r_s) also called the "top hat" function and Figure-7 displays the resulting spacetime warp metric for faster than light space travel.

These results compare the energy signature of a new method to warp spacetime shown in Figure-8 to the theoretical Alcubierre warp metric displayed in Figure-9 and Figure-10. Work continues using a laser to map spacetime around the experimental warp metric and clocks to measure time dilation within and around the proposed warp bubble.

Laser experiment used to map spacetime around the proposed warp drive demonstration device. This laser measurement system is mechanically and acoustically isolated from the system used to warp spacetime. Similar experiments are being designed using synchronized clocks to measure time dilation effects. No positive results to date.

The same experiment using a fog machine to trace a laser beam around the warp bubble disturbance. The laser beam was not deflected indicating spacetime is not being warped to any measurable degree by the proposed warp generator. Several configurations of the warp generator resulted in the same null result. The experiments are continuing using conventional energy sources to affect spacetime...

SPECIAL NOTE: The aim of these experiments was an attempt to show that a warp bubble could be generated using electromagnetic energy instead of negative energy as required by Alcubierre's faster than light warp metric. The method proposed to warp spacetime seems to match the signature warp bubble theoretically predicted using negative energy. General Relativity, Dark Matter and Dark Energy cosmology indicate that a warp bubble is analogous to expanding spacetime observed to occur between distant galaxies. In effect, expanding spacetime between galaxies is like a conveyer belt pushing galaxies apart at a rate of approximately 71 km/sec/mega parsec. While measuring the warp effect predicted by my method has not proven successful the paper by Alcubierre states the following, "The need for exotic matter therefore doesn't necessarily eliminate the possibility of using spacetime distortion like the one described here for hyper-fast interstellar travel." Therefore to continue this research, I have constructed a piezoelectric transducer to more accurately measure changes in inertial mass caused by spacetime distortion.

(2) GRAVITY AND CURVATURE OF SPACETIME
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.

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.

(3) TEST FOR FLATNESS OF SPACETIME
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.

(4) SPACETIME CURVATURE
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.

(5) GENERAL RELATIVITY THEORY AND APPLICATIONS
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 and isotropic 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.