If space has a hyperbolic geometry (unbounded universe), what will happen to two initially parallel flashlight beams as they traverse billions of light years of space?
A)They will remain parallel.
B)They will gradually diverge (move apart) to a maximum separation, and then gradually converge and cross.
C)They will gradually converge (move together) and eventually cross.
D)They will gradually diverge (move apart).

Question

Quizplus · Accepted Answer

In a hyperbolic geometry, parallel lines (or in this case, the paths of light beams) will gradually diverge from each other as they extend into the distance. This reflects the nature of hyperbolic space, where the geometry is such that the rules of Euclidean geometry (like the parallel postulate) do not apply in the same way, leading to diverging paths instead of parallel ones.

If Space Has a Hyperbolic Geometry (Unbounded Universe), What Will