Transwarp Drive
 
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Transwarp and the Transwarp drive were an experimental technology for increasing the efficiency and speed of starship propulsion systems. Though the project showed great promise and was extensively tested on the USS Excelsior, Federation scientists could not make it work successfully and abondoned the project.

An artificially created subspace tunnel, or Transwarp Conduit was used by a Borg ship of unusual and previously unknown design in 2369. The Tranwarp Conduit was capable of defying normal subspace limitations and allowed maximum speeds up to twenty times faster than a Galaxy class starship.
This series of transwarp conduits was accessed by an encoded high-energy tachyon pulse.

The actual method or process of using Transwarp drive and Transwarp Conduits is unknown and has not been stated in any show. However, a rare form of Dilithium, called "Trilithium" was used by the Voyager crew in an attempt to recreate the original Tranwarp experiments. Unfortunatly Voyagers tests ended in abject failure. The reason for this being the sudden and spontaneous occupation of every point in the universe when an object reached Warp 10, the theoretical barriar of warp drive.

There is speculation that the original Tranwarp drive was an attempt to create an opening via interphase and travel through another dimension. Since time flowedat a differant rate in this other dimesion a three week journey via interphase would only take three days in real space. However, this is only a stop gap measure and creates unpleasent senarios akin to the Relativity problems of non-warp interstellar travel.

Other theories include the possibility that the tranwarp conduits act as containment fields, much like the Transporters annular confinement field. This containent field would maintain the integrity of the object and keep it from spreading out to occupy every point in the universe. 1