The inversion drive was an alternate development of faster-then-warp travel that was being considered by the Federation and was field tested on the USS Enterprise under the command of Captain James T. Kirk in 2275. The technology was created by the Hamalki scientist, K't'lk, and utilized what could be called "creative physics."
While it was capable of intergalactic travel by sending a vessel through de Sitter space, the drive had several unforeseen side-effects. Inversion often caused hyper-realistic "visions" akin to intense "out-of-body experiences" in most humanoids, as well as a great deal of damage to the fabric of the universe. These effects made it so dangerous for use that the drive's development and any further research into the technology was discontinued. (TOS novel: The Wounded Sky)