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Sep15-10, 10:29 PM
The thing is, if you ignore the
relativity of simultaneity
, then Chalnoth is right. Isotropy without homogeneity would imply a privileged point of view. However, if everything is flying apart from the same event, then you have to do the full analysis with the lines (or planes) of simultaneity. You'll find that every plane of simultaneity for every particle intersects the worldlines of the other particles in such a way that you DO have isotropy from the Point of View of every particle.
But you don't have homogeneity in any particle's point-of-view, because each observer sees the density tend towards infinity at the outer edge of the sphere.
This isn't what homogeneity means. Homogeneity means that if I move to a different location, I see the same thing as if I stay put.