Warps Drive

Warp drive is a hypothetical faster-than-light (FTL) propulsion system which a spacecraft equipped with a warp drive may travel at apparent speeds greater than that of light by many orders of magnitude, while circumventing the relativistic problem of time dilation.

Warp drive technology creates an artificial "bubble" of normal space-time that surrounds the spacecraft. Consequently, spacecraft at warp velocity can continue to interact with objects in "normal space".

A valid solution for faster-than-light travel which models the warp drive concept, called the Alcubierre drive, was formulated by physicist Miguel Alcubierre in 1994. Subsequent calculations found that such a model would require prohibitive amounts of energy. However, it has recently been found that by changing the shape of the warp drive, much less energy could be used, making the idea of a warp drive once again feasible, and NASA scientists have begun preliminary research on such technology. 

By using a matter/antimatter reactor to create plasma, and by sending this plasma through warp coils,  a warp bubble is created which could be use to move a craft into subspace and hence exceed the speed of light. 
Warp engine technology as a 'Gravimetric Field Displacement Manifold' and the device being powered by an anti-matter/matter reaction which powers the two separate nacelles (one on each side of the ship) to create a displacement field (the aforementioned "bubble")

Warp drive velocity in Star Trek is generally expressed in "warp factor" units, which—according to the Star Trek Technical Manuals—correspond to the magnitude of the warp field. Achieving warp factor 1 is equivalent to breaking the light barrier, while the actual velocity corresponding to higher factors is determined using an ambiguous formula.

However, the velocity [in present dimensional units] of any given warp factor is rarely the subject of explicit expression, and travel times for specific interstellar distances are not consistent through the various series.

Warp factors are converted to multiples of c with the cubic function v = w³c, where w is the warp factor, v is the velocity, and c is the speed of light. Accordingly, "warp 1" is equivalent to the speed of light, "warp 2" is 8 times the speed of light, "warp 3" is 27 times the speed of light, etc.

A primary component of the warp drive method of propulsion in the Star Trek universe is the "gravimetric field displacement manifold," more commonly referred to as a warp core. It is a fictional reactor which taps the energy released in a matter-antimatter annihilation to provide the energy necessary to power a starship's warp drive, allowing faster-than-light travel. Starship warp cores generally also serve as powerplants for other primary ship systems.

When matter and antimatter come into contact, they annihilate — both matter and antimatter are converted directly and entirely into enormous quantities of energy, as electromagnetic radiation. In the Star Trek universe, fictional "dilithium crystals" are used to regulate this reaction. These crystals are described as being non-reactive to anti-matter when bombarded with high levels of radiation. Usually, the reactants are deuterium, an isotope of hydrogen, and antideuterium (its antimatter counterpart).

The warp core reaction chamber is often referred to as the "dilithium intermix chamber" or the "matter/antimatter reaction chamber", depending upon the ship's intermix type. The reaction chamber is surrounded by powerful magnetic fields to contain the anti-matter. If the containment fields ever fail, the subsequent interaction of the antimatter fuel with the container walls would result in a catastrophic release of energy, with the resultant explosion capable of utterly destroying the ship. Such "warp core breaches" are used as plot devices in many Star Trek episodes.