Expansion: A 2D Spherical Example


Consider a two-dimensional spherical surface upon which we have a collection of 2D galaxies. Notice the lines of latitude: these are our comoving coordinates. Now let's have this sphere expand a bit:


Notice that the galaxies stay the same size and in the same position relative to the lines of latitude and longitude (comoving coordinates stay constant). But because the sphere has expanded, there is now a greater distance between each galaxy. The further away two galaxies were at the start, the greater their separation now. This is the Hubble Law.


More expansion simply increases the effect. Everything scales up equally, all observers see a Hubble Law with galaxies appearing to move away from them. But no galaxy is truly at the center of this expansion. There is no center on the surface of the sphere. (Yes, there is a center of the sphere in the third dimension, but there is no requirement in geometry that such higher "embedding" dimensions exist. The 2D spherical surface is a perfectly consistent, self-contained geometric entity.)