Gravatational Propulsion: Simple I've read many of the messages posted and decided I would add some comments and more importantly action myself (and hopefully some of you ) to find the answer to some fairly simple questions that will put the problem to one of required energy, energy generation and then materials and methods I think along the lines of what many of you are discussing.
Space is big particularly if your not moving. It gets shorter if you travel fast relative to a stationary observer but not short enough. The speed of light is constant in all reference frames. Both these postulates appear to us to be true. Fermi Lab, Cern and even your watch on a 747 (if you fly long enough) demonstrate that moving clocks tick slower, lengths contract, particles last longer if moving relative to statinary observers etc.
Taking one small step further from the Special Theory, where things get shorter or longer depending on who's observing what , we need to consider the path objects travel on in "space", specifcally spacetime, and what effects these paths.
Consider a sphere. Imagine that we all live in the skin (very thin) of this sphere. The sphere is expanding, which is why everything in space looks like it's traveling away from us, as caused by initial energy, the Big Bang, of the universe. The degree of curvature of this sphere is determined by the amount of energy. We can imagine the curvature of the sphere to be a three dimensional shadow in 4 dimensions adding time..and determined geometrically by a metric R^4: (Sqrt[dt^dt + dx^dx + dy^dy + dz^dz] some mass and some imposed rules to deriive the shape ...
Carl Sagan desribed spave  time and the curvature of our sphere, and its influence on moving massive bodies I think best describing a bowling ball placed at rest in the center of a trampoline. The bowling ball represents mass, that has the effect of bending spacttime (the tranpoline) which in terns defines the path of a rolling tennis ball released at the edge of the trampoline. The tennis ball orbits the bowling ball as defined by the curvature of the trampoline. In the same way our planets orbit the sun as defined by the suns mass and it's effect on the curvature of space time it exists in locally relative to our planets and passing objects including photos/light.
Kepplers equation of motion can be exactly derived in terms of the motion of massive bodys around the sun via the potential (GMm/r) that describes the force between the sun and planets. Equivalently, the mass that the sun provides can be calculated into the fabric of spacetime curvature (of our trampoline). A farily straight forward geometry calculation (motion of our tennis ball) to then derive the geodesics on this curved manifiold will yield the same equations of motion of the masses around the sun. The result is pretty cool as the equations of motion derived in terms of curvature and geometry in this way can be represented by a single Kristoffel symbol...Einsteins expresion of differential equations, a notation that he admitted his best contribution to science.
Anyway, the important point to recognize is that mass bends space time. Mass is equivalent to energy. If we treat spacetime as an object, we can derive equations of motion along the paths that spacetime and the bending that mass/energy define. This is done most dramatically in the study of black holes and orbits of matter and radiation around them where the entire mass of a star is equated to energy and curvature from a point source the size of a pea....ie, the curvature is very great not even allowing light to escape beyond a radius from the source defined by the stars original mass before collapse......A very big bowling ball.
In deep space, not perturbed by local variations of mass like planets, black holes, dark matter etc...light travels along lines that are defined by the general curvature of our universe..the 3 deg K background reminant of the big bang. Locally, where massive objects are present, light has been observed to bend locally. We now observe not only light bending around are own sun but even moving black holes detected by the disruption of observed postion of objects between us and the source the hole passes between.
Back to the question of travel. Obviously the question is'nt how we go faster, but how we shorten the path. Light can be made to travel as fast as we want. the speed of light only defines the speed limit in the curved space that we produce. The bigger the bowling ball (energy), the more curvature we produce....Here's some questions that we need to answer:
Can R^4, our best/favorite defined spacetime manifold..pick a metric, be bent in such a way to bring two points closer together....say between here and alpha centari.
Assuming that our physicist/geometrists friends come back with a solution, they likely will, we will need the solution as a function of curvature, or bending, at least locally relative to our ship that will create the mapped curvature solution from a to b.
Once we have the curvature required to follow our "light" path, we can equate the curvature immediately to energy. That energy will be required to be produced and focused taking account for any local curvature produced in proximity (open space or in proximity of another curvature source such as a planet).
Now that we have the required energy solved we look for a source. Be aware that the mass (energy) of a star that can collapse to the size of a pea to create the amount of curvature to create a black hole is enourmous...We're going to need alot of energy. Matter  Anti matter (we make anti matter all the time) works as it's 100% efficient but were going to need something massive that can produce it on small realtive scale. Any ideas ? A materials problem.
With the energy problem solved, we now need to manipulate it generating a field and phase necessary to control direction...bad term as we basically don't move anywhere...another problem for our geometrists.
Simple.
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