Ant On A Rubber Rope - Applications of The Problem

Applications of The Problem

See also: Metric expansion of space

This problem has a bearing on the question of whether light from distant galaxies can ever reach us if the universe is expanding. If the universe is expanding uniformly, this means that galaxies that are far enough away from us will have an apparent relative motion greater than the speed of light. This does not violate the relativistic constraint of not travelling faster than the speed of light, because the galaxy is not "travelling" as such—it is the space between us and the galaxy which is expanding and making new distance. The question is whether light leaving such a distant galaxy can ever reach us, given that the galaxy appears to be receding at a speed greater than the speed of light.

By thinking of light photons as ants crawling along the rubber rope of space between the galaxy and us, it might seem that just as the ant will eventually reach the end of the rope, given sufficient time, so the light from the distant galaxy will eventually reach Earth, given sufficient time. This, however, ignores the fact that the metric expansion of space is accelerating. An ant on a rubber rope that expands faster than linear is not guaranteed to reach the endpoint.

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