Warp drive

A warp drive is a spaceship propulsion system allowing it to travel at speeds faster than light by many orders of magnitude. The spaceship does not actually travel faster than light but rather a high-energy warp core reactor is used to compress 4d spacetime in front of the ship (so it contracts), and decompress spacetime behind the ship (so it expands), creating a warp of spacetime and displacing the ship forward, propelling it along like a surfboard on an expanding wave of spacetime. This solves the special relativity dilemmas and ensures that there are ordinary velocities, there is no time dilation, and no prohibitive fuel cost.

This Alcubierre warp drive theory was first suggested by Miguel Alcubierre, stating that to build one would require negative energy and exotic matter, the same stuff needed to maintain stable wormholes.

In Star Trek: Federation warp drives were fueled by the reaction of matter (deuterium) and antimatter (antideuterium), which produced a highly energetic plasma, which was channeled through conduits and field-generation warp coils to create a warp field. This is a subspace displacement field which warps spacetime around the vessel, encompassing it in a subspace bubble, allowing it to "ride" in this distortion and effectively travel faster than the speed of light. The displacement "ride" had the effect of reducing the inertial mass of the spaceship, which required inertial dampers to control.

Dilithium crystals regulate the matter-antimatter annihilation rate, because they are the only form of matter known to be “porous” to antimatter. Antihydrogen atoms are threaded through the lattices of the dilithium crystals and therefore remain a fixed distance both from atoms of normal matter and one another. In this way, dilithium could regulate the antimatter density, and thus the matter-antimatter reaction rate.

This is in contrast to other faster-than-light technologies such as a jump drive where travel is in hyperspace lanes and are much faster than warp drives as you could jump from point to point down these lanes almost instantly, taking multiple jumps to get to a destination. Warp involves a measurable passage of time using an exponential scale called "warp factor" where a factor of 10 is infinite speed. Spaceships at warp velocity would continue to interact with objects in "normal space".