- #1
Warp
- 128
- 13
From answers given to me here and elsewhere, I finally got a (what I think should be the right) answer to the problem:
Suppose that the universe were expanding in such a way that two planets were receding from each other at a constant speed of 1.1c (or, in other words, their distance would grow at a constant speed of 1.1c). Assume that one of the planets sends a light ray to the other. Will the light ray ever reach the other planet?
Quite surprisingly and rather unintuitively, the answer seems to be yes: The light ray does reach the other planet eventually, even though that planet is receding faster than c. The mechanism behind this lies in how the geometry of the universe is changing, and is easiest understood with an analogy: If there's an infinitely stretchable rubber band with a snail on one end, and the snail advances 1 meter per hour and the rubber band is stretched 1.1 meters per hour, will the snail ever reach the other end? The answer is yes.
This got me thinking: The snail reaches the other end because it's effectively traveling faster than 1 m/hour (because the stretching rubber band is "pulling" the snail).
Doesn't it likewise mean that the ray of light is effectively traveling faster than c, or else it would never reach the other planet?
Does this mean that the speed that light effectively travels is larger in an expanding universe than in a (hypothetical) steady-state universe? (And conversely, light would travel slower in a shrinking universe.)
If the answer is yes, then what consequences does this have to the definition of c?
Suppose that the universe were expanding in such a way that two planets were receding from each other at a constant speed of 1.1c (or, in other words, their distance would grow at a constant speed of 1.1c). Assume that one of the planets sends a light ray to the other. Will the light ray ever reach the other planet?
Quite surprisingly and rather unintuitively, the answer seems to be yes: The light ray does reach the other planet eventually, even though that planet is receding faster than c. The mechanism behind this lies in how the geometry of the universe is changing, and is easiest understood with an analogy: If there's an infinitely stretchable rubber band with a snail on one end, and the snail advances 1 meter per hour and the rubber band is stretched 1.1 meters per hour, will the snail ever reach the other end? The answer is yes.
This got me thinking: The snail reaches the other end because it's effectively traveling faster than 1 m/hour (because the stretching rubber band is "pulling" the snail).
Doesn't it likewise mean that the ray of light is effectively traveling faster than c, or else it would never reach the other planet?
Does this mean that the speed that light effectively travels is larger in an expanding universe than in a (hypothetical) steady-state universe? (And conversely, light would travel slower in a shrinking universe.)
If the answer is yes, then what consequences does this have to the definition of c?