Normal Space
In normal 3-D space, the "shortest path" between two events A and B is by traveling in a straight line. Because of relativity, there is no such thing as universal time: so let the time be measured with respect to a clock whose motion matches the space-time path. Call this space-time path "P". Then the shortest path in space is simply the path in space traced by the space-time path P.
In strict mathematical terms, it may be impossible to define such a path, along which matter can travel. However, it usually is possible to find an infinite sequence of paths that converge uniformly to some limit, that is, some "limiting" path. Of course, under relativity, matter may not be able to travel along this limiting path, but light can travel along this path. In fact, the path of the light beam from A to B is the theoretical limit. No ship in normal space could follow the path of light in 4-D space time, but it can get arbitrarily close (until the energy required to go any faster exceeds the energy available).
This path (or limiting path) may not be unique: there may be many "shortest paths." Also, no path may exist; for example, suppose A lies in a black hole and B lies outside the black hole—since nothing can exit a black hole, such a path would not exist. Finally, because of general relativity, this path is not a "straight line" in the strict Euclidean sense, but is "curved." For example, if we aimed a rocket at the Moon traveling near the speed of light, the shortest path to the Moon is still a curved path. In fact, even if we aimed a photon of light at the Moon, it will follow a curved path, since gravity bends all things. The space along which the photon travels is, in fact, curved because gravity curves space itself. Just like traveling along the surface of water; if the surface of the water is swelled in a wave, then it would still be possible to travel in a straight line through the water (traveling underneath the wave,) but it would require more effort than just traveling along the curved surface of the water. It is still possible to travel in a straight line to the Moon, yet since the curved light beam is the best, the curved path close to this beam (following the path of the curved space) is better than the straight path. This is because the light beam is technically actually traveling in a straight line, relative to the curved space it is traveling in, but the space itself is curved, so it appears to an outside observer that the light beam is traveling in a curved line. Of course, if we take energy expenditures into account, then the minimum energy paths are just transfer orbits and gravity boosts that Earth space agencies predominantly use although these are not 'fast'.
Read more about this topic: Hyperspace (science Fiction)
Famous quotes containing the words normal and/or space:
“Our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different.”
—William James (1842–1910)
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
—Isaac Newton (1642–1727)