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Re: Invisible

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Posted by Zephram Cochrane/">Zephram Cochrane on November 22, 1999 03:06:55 UTC

: If you were looking strait at something and it accelerated away from you to the speed of light, would you be able to see it? wouldn't the light not be able to catch up to it and therefore not reflect back to you?

Lets say the rocket accelerates away under a constant proper acceleration. You could look at this in a couple of ways, first... It would asymptotically approach the speed c. In fact is you were to graph its position as a function of time, it would be hyperbolic. This asymptote with a slope c that it approaches crosses the position axis beneath the starting point of the ships acceleration. Since all light rays will have a slope c, non of them originating beneath this asymptote will reach the ship. This asymptotes intercept is a distance c2/a below the ships starting point. This means that the ship can't see anything behind this distance. In fact if we fired a laser at the ship below this distance, it would never catch up to it. However, we would still be able to see the ship because of light that was initially above that distance and we could see light that the ship itself emanates.

The second way to look at this is to say that the ship is being held still by the engines in a universe with a uniform gravitational field that pulls every thing else down the other direction. The scaling of space that leads to the simplest metric for this space-time results in an invariant interval of ds2 = (1 + az/c2)2dct2 - dz2 - dr2 - r2df2

This metric has an event horizon at z = -c2/a

This gives the correct distance behind the ship at which light won't catch up to it.

The ship never reaches c, but the asymptotic behavior of its flight does lead to an effect close to what you are thinking.

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