The Theory of Infinite Velocity was a theory in warp physics.
The theory held that traveling at warp ten was a theoretical impossibility, as one would then be traveling at infinite velocity, and therefore occupy every point in the universe simultaneously. One would be able to go any place in the wink of an eye, and time and distance would have no meaning.
After a 2372 transwarp test flight aboard the shuttle Cochrane, data suggested that the theory might be correct. However, traveling at infinite velocity also unexpectedly appeared to accelerate the natural human evolutionary process by millions of years. (VOY: "Threshold")