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Can We Travel Faster Than Light?

Physicist Thomas Roman of Central Connecticut State University offers the following response:

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.
 Animation: Kenneth Jones FASTER-THAN-LIGHT TRAVEL, depicted in series such as Star Trek, is not possible--except for maybe inside a spacetime or Alcubierre warp bubble.

In curved spacetimes, when we compare two observers at large separation, we can no longer use the "locally flat" approximation. In the plane-and-sphere 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 light--relative to observers inside the bubble. Outside the bubble, spacetime is also flat and no particle can travel faster than light--relative 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

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