Einstein's special theory of relativity predicts that nothing can exceed the speed of light. But special relativity applies when spacetime is flat. When spacetime is curved, the theory applies only "locally"that is, over regions of spacetime small enough to be considered flat. Consider the analogy of a plane that is tangent to a sphere. The flat geometry of the plane is a good approximation to the geometry of the sphere when the size of the plane is very small compared to the sphere's radius of curvature.
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In curved spacetimes, when we compare two observers at large separation, we can no longer use the "locally flat" approximation. In the planeandsphere analogy, this situation would correspond to comparing two observers on the sphere separated by a distance comparable to the sphere's radius of curvature. Although each observer could approximate the geometry in his or her local region as a plane, there is no single plane that would be applicable to both observers. Consequently, the two observers in curved spacetime can each apply special relativity in their own local region, but not globally.
A similar situation arises in an expanding universe. Here one should not think of the galaxies as moving through space, but rather that the space between the galaxies is expanding. Einstein's general theory of relativity, on which such models are based, imposes no restrictions on the rate at which the expansion of space can drive the galaxies apart. But special relativity still applies locally, in the sense that a particle chasing a light ray can never catch up to it. An analogy is to imagine bugs crawling on a rubber sheet. By stretching the sheet we can make the bugs recede from each other at arbitrarily high speeds, but no bug can crawl across the sheet faster than a light beam.
In serious proposals for "warp drive," such as the Alcubierre warp bubble, space is flat inside the bubble and special relativity applies. In this region, nothing can travel faster than lightrelative to observers inside the bubble. Outside the bubble, spacetime is also flat and no particle can travel faster than lightrelative to observers outside the bubble. But because of the large expansion and contraction of the spacetime in the wall of the bubble, the inside of the bubble can move faster than light relative to the outside. This would also be true of light rays inside the bubble; they would be carried along by the spacetime warp, too. What causes this mismatch of the two flat spacetime regions is the large spacetime curvature in the bubble wall that separates the regions.
Cosmologist Martin Bucher of the University of Cambridge adds this insight:
In the preEinsteinian conception of the nature of space and time, there is no limit in principle to how fast an object can travel. But in Einstein's special theory of relativity, the notion of causalityof the past completely determining the futurewould break down if any type of matter, energy or signal were able to travel faster than light.
In the preEinsteinian framework, time has an absolute character. The time of an eventand thus its time orderingis the same to all observers; velocities add according to ordinary addition. For very small velocities (small compared to the velocity of light), the same holds in relativity, but for large velocities significant modifications occur. Early in the 20th century the MichelsonMorley experiment established that the speed of light is the same to all observers whatever their relative motion. Therefore the law for adding velocities must be modified. The relative velocity of two objects, one traveling at the same of light and the other traveling at sublight speeds, must equal the speed of light. When both are traveling at sublight speeds, the relative velocity must be less than the speed of light.
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One surprising consequence is that time loses its absolute character. The times perceived by observers moving with respect to each other do not coincide. But observers always agree on the ordering of events. If we admit the possibility of fasterthanlight speeds, some observers would perceive one event as occurring before another, others would perceive them as occurring simultaneously, and a third group would perceive the reverse order. The time ordering is invariant only when the two events can be linked by a signal traveling at a speed slower than or equal to the speed of light.
In the context of an expanding universe, it is often stated that widely separated points move apart faster than the speed of light. At first sight this would seem impossible. But an expanding universe must be considered within Einstein's general theory of relativity, a generalization of the special theory of relativity. In general relativity, motion relative to the speed of light is defined locally. The separation between two distant points can increase faster than the speed of light as a result of the swelling of the intervening spacetime. Nothing can pass through the space faster than light, but space itself can carry things apart superluminally.