This paper describes one possibility for rapid round‐trip, paradox‐free Faster‐than‐Light (FTL) travel between Earth and distant stars within the human lifetimes of those on‐board the ships and Earth. It shows that such rapid transits would require dimensions beyond the 4 dimensions of flat or curved spacetime; with the added dimensions needed to give starships (their worldlines) room to “climb” and “descend” above the spacetime realms of Special Relativity (SR)—realms where nothing travels faster than the speed‐of‐light(c). The added dimensions would be associated with zero‐point field gradients formed within the quantum vacuum by actions of specially conditioned em radiation emitted from accelerating ships. These gradients would result in: STL (slower‐than‐light) vehicle velocity within the perturbed vacuum surrounding the ship; FTL vehicle velocity with respect to the unperturbed vacuum and Earth; and invisible FTL vehicle travel in all observer‐frames that move STL with respect to Earth. For one case of FTL travel, rapid transits to distant stars would result in starship disappearance from human sight after light speed is reached—followed soon thereafter by its reappearance trillions of miles away, in close proximity to its target star. And during the short interval of disappearance, the starship’s worldline wouldjumpover trillions of miles of distance—arching like a suddenly‐formed rainbow within a “spacetimetau” realm of existence that rises above curved or flat spacetime terrain. © 2004 American Institute of Physics