Exploring has been one of our defining characteristics as species, and being outer space infinitely more vast than Earth it is a matter of time since we will begin travelling to the stars; to do that it is necessary to develop means to travel faster than light, something that seems closer to reality since Miguel Alcubierre demonstrated the theoretical feasibility of that.
Every high school physics teacher would tell students that no one can surpass the speed of light according to Albert Einstein and his theory of relativity. However, that's only partially true: Einstein produced two grand theories that treat roughly about the same topic, are interdependent, but deal with different things and scales. The "special theory of relativity" deals with phenomena at a local scale while the "general theory of relativity" sees the matter at a universal or cosmological scale. Simply put: the special theory deals with the small - so to speak - while the general one with the really big thing out there. This is a rough approximation, of course.
According to the special theory of relativity, indeed c - the letter with which conventionally the speed of light is identified - cannot be surpassed but, bear in mind, this is a local limitation in space-time. Within the context of the general theory of relativity things are different and what Dr. Alcubierre did was to demonstrate that and how such a fact could be used to travel faster than light without violating the special theory. His seminal work explains essentially that it would be possible to compress space-time ahead of a spaceship and expand it on its tail. The ship would be inherently motionless inside what reminds us of a "Warp bubble" of science fiction, and it is exactly that. The ship would not be violating any physical law; it is just that the space will be changed around - or in front - of it. This is the mythical warp drive.
The original work of Dr. Alcubierre has several limitations; he acknowledged some even in the same paper in which he made public his findings and other authors and scientists have elaborated on that since 1994, when the Mexican physicists published it. However, many other scientists, also taking into account what their colleagues observed as contradictions or limitations have further elaborated on the Alcubierre metric and found that it is theoretically possible to build a warp engine. There are of course, many and very significant hurdles that will have to be surmounted first.
The investigations and considerations of Krasnikob, Van der Broeck, the ESAA group and NASA itself added a lot to the original work by Dr. Alcubierre. Nevertheless, this issue is far from solved but all those papers at least serve as a very good staring point. Of course, when something as avant-garde as suggesting today that travelling faster than light is possible comes into the limelight, scientific facts may get mixed with unsound theories, science fiction or baseless ideas. The work of NASA in this regard has been very important by providing some management rules for such out-of-the-box investigative efforts with a simple protocol in mind: Making interstellar travel practical at human time scales, because while it is also possible that a man-made ship of today's current technological levels would eventually reach other solar systems, it would take it tens of thousands of years. The idea of a warp drive is to reduce that time to a few days or months.
According to the works of Einsten, time slows down inside a ship approaching the speed of light as related to an observer on the departure or arrival points. But this is different: Time inside a warp ship would not be altered in relation to external, distant observers, so, such a way to travel wouldn't be much too different than taking a ride in an Apollo capsule to the Moon, only that in the same time it took those astronauts to reach our natural satellite, future travellers will certainly go as far as the available energy allows them, which is at any rate, far, far more than conventional, chemical rockets can achieve today.
The topic is naturally very complex because the metrics associated with faster-than-light travel (FTL) and these models - a metric is basically a system to calculate distances in multiple dimensions - invariably tell us that we would need exotic energy to achieve warping. Using wormholes is another suggested method for FTL, but in reality it is closely related to using warp engines: There are mathematical indications in the sense that a warp bubble inside of which a spaceship could travel is in essence, a special case of a wormhole, and keeping wormholes opened and stable would require also. in any case, exotic energy which - you guessed - is not exactly the same flavour of juice used in your car's battery and is not particularly easy to produce in the scales that would be required for interstellar travel, yet.
Exotic energy is something from outside our reality; we know it exist because taking it into consideration mathematically solve a number of equations that otherwise would be impossible to prove right. Then, in our world and at a macroscopical scale it can be detected thorough the very simple and bizarre Casimir effect (discovered by Casimir and Polder): Just put two semiconductor surfaces very close together, and forces will begin to form between the plates spontaneously. They are minute and very sensitive equipment is required to actually measure those forces, but they are there and there is no other explanation than exotic energy popping into existence between the plates.
This and the mighty metrics that I told you about seem to suggest some additional things that are being considered by people like Stephen Hawking: It seems now that our little universe is part of something even grander, called a "multiverse" or "super cosmos", inside of which universes are created and blow up like bubbles in foam. Dr. Hawking even suggested that a sufficiently advanced civilisation could eventually escape certain doom at the end of the universe by assign into another one.
We will sooner or later travel to the stars and even further, and if you believe that what I am telling you is bogus science fiction, just read the articles linked to this page and the bibliography that I present for your consideration.
Bibliography and references:
"The Warp Drive: Hyperfast Travel Within General Relativity" - M. Alcubierre - Class.Quant.Grav.Letters 11, L73-L77 (1994.)
"The Unphysical Nature of Warp Drive" - M. Penning, L. Ford - Institute of Cosmology, Department of Physics and Astronomy, Tufts University / Class. Quantum Grav. 14 1743-1751 (1997.)
"A Warp Drive With More Reasonable Total Energy Requirements" - C. Van den Broeck - Instituut voor Theoretische Fysica - arXiv:gr-gq/9905084v5 (1997.)
"Hyperbolic Geometrodynamic WarpDrives & Beyond" - P. Hoiland, E. Halerewicz - ESAA/ATPG - ESAA (eBook) (2003.)
"Breakthrough Propulsion Physics Project: Project Management Methods" - M. Millis - NASA - TM 2004-213406 (2004.)
"Warp drive with zero expansion" - J. Natário - Instituto Superior Técnico, Portugal / Class. Quantum Grav. 19 (2002) 1157-1165 (2002.)
"Study of Vacuum Energy Physics for Breakthrough Propulsion" G. Maclay et al. - NASA - CR-2004-213311 (2004.)
"An Assessment of Faster-Than-Light Spacetimes: Make orBreak Issues" - E. Davis - Institute for Advanced Studies at Austin, Austin, Texas - AIAA 1006-4908 (2006.)
"Warp Drive: A new approach" - R.K. Obousy, G. Cleaver - Baylor Univ. - arXiv:0712-1649v6 (2008.)