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Originally Posted by robertgrunberg
This ultimately elegant equation says that the universe is spherical and its diameter increases at 2c.
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I think you may be missing the point of differential geometry here. The expansion of the universe is not like the expansion of a solid object embedded in our universe (like watching a balloon expand as you inflate it), but is actually an expansion of the manifold itself (like being a two-dimensional creature living on the surface of the balloon as it inflates, except in quite a few more dimensions). In other words, there is no "edge" to the universe and no "outside" for the edge you describe to move through.
And I'm not an expert, but I think you may be getting things horribly wrong from the get-go by using anything to do with Euclid (real space-time is non-euclidean), the model of an acoustic medium is not one I'm sure you can justify because of this (as well as many other reasons, including the requirement for an aether), and V=(cT)^3 isn't the volume of an expanding sphere. I'm still not sure what "the inverse square law is intrinsic" has to do with the price of bread here. And I don't see how you explain the non-uniform character of the background radiation either.