To support the rapid-action pace of Star Trek, a way to get from location A to location B in a timely manner is very necessary. If the crew of the Enterprise receives an emergency signal, they need to reach their target destination before the ship that sent the signal is long gone and whatever enemy that was threatening them is an extinct race. The series is set in the Milky Way, which is about 100,000 light years across. Traveling even a fraction of that distance at the speed of light would still see thousands of years passing from an outside perspective. The writers needed a way to get around this potentially huge plot hole while still maintaining a vague adherence to the laws of physics. Since they knew from the theory of special relativity that it's not possible to travel faster than the speed of light, they developed an alternative. Instead of the ship moving through space at an impossible speed, the ship pulls and bends space around it to reach its destination. This way, they can avoid the restrictions imposed by relativity. Relativity only applies to objects moving through space, not space itself. A theoretical "warp drive" would be able to contract spacetime in the direction of desired travel, while expanding it in the opposite direction. The ship, remaining stationary, can "warp" great quantities of spacetime around it to effectively "travel" immense distances fairly quickly.
The writers developed a system of "warp factors" to quantify this in terms of the speed of light:
|Warp Factor||Number of times the speed of light|
Even while using this highly theoretical method of travel, they imagined a limit for it, described as the impossible "Warp 10".
Is it possible outside of science fiction? NASA thinks maybe, eventually. Many scientists have done extensive research into it, as it would mean distances that were previously scientifically of the question could become possible. One such theoretical real-world equivalent that has been explored is the Alcubierre drive. Conceptually nearly identical to a warp drive, it has been proven to be mathematically sound, though that doesn't guarantee physical possibility. Initially, the calculation for it involved more energy than present in the observable universe, but has since been scaled down to about the energy equivalent of three solar masses, or around 3144 times the mass of Jupiter.
A second technology that is necessary for the Star Trek universe to form a cohesive storyline is an ansible. When traveling distances of the scale allowed by warp drive, communication becomes an issue. Radio waves, which travel at merely the speed of light, would take the equivalent light years between ships or planets to be received. A distress signal could take tens or hundreds of years to reach its intended receiver even at many times the speed of light. This is circumvented by sub-space communication, with a device typically given the general name "ansible" in science fiction. An ansible could theoretically work by two methods. The first is by the creation of a "micro-wormhole", or a tiny shortcut through spacetime. Signals sent through this could reach their target in a fairly timely manner, depending on the location of the wormhole. The second option is through the phenomenon of quantum entanglement, where a pair of particles are "entangled" in such a way that a change in the state or orientation of one particle will affect the other, regardless of space or time. Measurements of the properties of entangled particles have found that they are appropriately correlated. For example, if one is spinning clockwise, the other will spin counterclockwise. Manipulating the spin of one would affect the spin of its counterpart, The particular usefulness of this is that messages could possibly be sent this way through a kind of binary system. At a delay of a hundredth of a percent of the speed of light, communication would be near-instantaneous. It has been argued that this would affect causality, and therefore would not be possible in practice, however predictions of the connection between entangled particles have been experimentally proven. It seems that the largest issue would be in developing meaningful communication through this method.