The Phoenix breaking the warp barrier.

A schematic of the Malcorian warp ship.

The warp barrier, also known as the light barrier, was the transition from sublight velocities to faster-than-light warp speeds. It was also used as a reference to the limits of warp drive technology to achieve certain rates of speed.

In 2063, the Phoenix reached the warp threshold and broke the warp barrier. (Star Trek: First Contact)

In 2143, the NX-class prototypes broke the warp 2 barrier. (ENT: "First Flight")

In 2254, when the crew of the USS Enterprise discovered what they thought were survivors from the SS Columbia, which had crashed on Talos IV in 2236, José Tyler noted that the survivors would not believe how fast they could get back to Earth, due to the breaking of the "time barrier" that had occurred since the Columbia had crashed. (TOS: "The Cage")

This term suggests a similar correlation as with how warp factors of the same time period were referred to as "time warp" factors – a case of the writers still establishing terminology, and as such, the limitations in warp speed that were broken through this barrier was not stated in "The Cage".
However, given that according to ENT: "These Are the Voyages...", starships in 2161 were capable of warp 7, evidence of contemporary achievements can be found in TOS: "Arena" and "The Changeling" (both set in 2267), where it was established that it was while it was risky to sustain a speed of warp 7 or above for the Enterprise, the warp drive was capable of achieving warp 9.
According to the Star Trek Maps, the time barrier was in fact broken in the year 2243, due to improvements in matter/antimatter engine design, which made it possible to use more powerful warp field generators.

In 2364, after a series of formula modifications by Kosinski, the USS Enterprise-D experienced a phenomenal surge of power during a warp speed experiment and jumped over millions and later over a billion light years through space in a matter of minutes. During the first jump, instrumentation indicated that the ship actually surpassed warp 10, apparently making the so-called warp 10 barrier meaningless. Kosinski declared that science would need new definitions and new parameters to define warp speed. One suggestion was the Kosinski scale. It was later determined that the enormous surge of speed was caused by The Traveler and that Kosinski's formulas were bogus. (TNG: "Where No One Has Gone Before") The Traveler had the ability to alter warp fields using the energy of his thoughts to move through space and time. (TNG: "Time Squared", "Remember Me")

According to Star Trek: The Next Generation Technical Manual (p. 55), the ship didn't actually surpass warp 10, but did achieve the speed of about Warp 9.9999999996. This would be confirmed in VOY: "Threshold", where Tom Paris becomes the first Human to travel at warp 10, eight years after the events of "Where No One Has Gone Before".

In 2372, the warp 10 maximum warp barrier was also known as the transwarp threshold. (VOY: "Threshold")

See also

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