The long article by Shawn Williams on this topic is very interesting with a good introduction to non-Euclidian geometry. One can, however, disagree with some of the bases of various arguments.
There are definite flaws in Dr. Einstein's Relativity ideas. If they are examined closely, it can be seen that Einstein's Special Relativity work describes how information, or energy, sent from a transmitter to a receiver is distorted by relative motion of the two. The equations and ideas are accurate for this purpose but have no relation to what one could call, "Theory of How Everything Is," which seems to be the way the ideas are taken. The same criticism extends to his General Theory of Relativity wherein he extended the ideas to accelerated systems. This, too, would belong more properly in the theory of information interpretation rather than in physics.
Space-time as an entity which can be "warped," can be considered as a misapplication of a "four-dimensional historical locator" as if it were a physical reality. Time, perhaps best considered as a descriptor of sequence measured with reference to some repetitive motion having a constant phase, is considered as one dimension. The three dimensions of space must be specified to locate a historical happening in the time dimension. That is one must tell where-space- and when-time-to locate a particular incident in history. This again is information theory rather than physics.
However, it has been argued that since mathematical space always includes dots, and "Time," in practice, always is referenced to a cycle, the mathematics of "Space-Time" actually describe happenings in s substance made up of tiny units which have cyclical motions. As such Einsteinian Space Time is probably describing some such substance as is postulated in Oscillator/Substance Theory. (For more on this topic, you can check out the web site: http://groups.google.com/group/oscillatorsubstance-theory).
Likewise, Quantum Mechanics, a mathematical construct based on the known fact of quantization, is a mathematical model, not a physical reality.
A recent model of "Existence," postulated that all of our physical universe may be explainable in terms of two kinds of motion in a dot matrix. What we label, "mass" as being a manifestation of point-centered motion, and "energy" as being what is observed when there is motion within the matrix along a vector. It is postulated that two "sizes" of stable
3-D vortexes can exist within this matrix. With the smaller, more compact vortex type, which we know as "electron" or "anti-electron" convertible to the much larger, heavier but far less dense vortex type, the "proton" or "anti-proton." This model is in it's earlier stages of development. work on it thus far suggests that in many ways it will reach many of the same conclusions as "Space-time" and "String Theory" models do while explaining some things which the other models do not. However, unfortunately, there is nothing in this model to suggest that one can reverse sequence to go back in time or to do a space warp for anything bigger than a proton.
The model mentioned above initiated thinking which, has, since the original version of this article was written, evolved into The "Oscilator/Substance Model" referenced above. Space-Time Warping and Quantum Mechanical Tunneling may have possible explanation in the context of that theory.
Although, barring further information, we must conclude that the use of space and time warps for practical time/space travel is in the realm of science fiction, the idea of hyper-light velocities is not. The idea that an "infinite" amount of energy would be necessary to accelerate a particle-or "space-ship"-to beyond the speed of light is due to misapplication of Einstein's ideas. Einstein's Relativity Equations apply to the limits of information transfer in one "Perceptual Universe," the one which we most examine, in which the speed of light is the maximum velocity of a carrier wave, Einstein's Relativity ideas have no validity when applied to relative velocities of freely moving objects nor to the maximum velocity along a predetermined vector of a "space ship" having an internal engine.
It is true enough that we have no way known to transfer information or energy from an external source to an object moving away at the velocity of our carrier wave-a packet has an impossible job of out-running the mail truck... However, we could accelerate something to very close to the speed of light from an external source and then "kick in the after-burners" of an internal engine to get the extra kick to try to go beyond. With advances in nanoscience it may be possible to do some space exploration at hyper-light velocities in the not too far future.
A re-examination of the idea of what the speed of light is suggests that the speed of light is the average velocity in any given direction of all of the motions of the involved particles which pervade reality. As such, while it is not a maximum possible velocity of anything, it is probably a practical limit to the velocity at which any aggregate of units of the the "Substance of Existence," i.e., what we call matter, could be moved....