Exploring the Finite & Unbounded Universe: The Preferred Frame

[edpell]

If the universe is finite and unbounded why can not we think of the frame that sits with it's origin at the center of the 4-D sphere as a preferred frame? The preferred frame?

 

[bcrowell]

If the universe is finite and unbounded why can not we think of the frame that sits with it's origin at the center of the 4-D sphere as a preferred frame? The preferred frame?

When you embed an n-dimensional space inside an (n+1)-dimensional space, the extra dimension isn't actually there. It's just a mathematical convenience, and if you didn't want that mathematical convenience you could just treat the space as a 4-dimensional manifold. The center of the sphere isn't a physical point in space.

Regardless of whether the universe is closed, cosmological models have a preferred frame, which is essentially the frame in which the average Doppler shift of the CMB vanishes. There is a difference between a preferred frame built into the laws of physics (as in aether theories) and a preferred frame that is a feature of the spacetime metric and the matter inside it. The former contradicts GR. The latter is expected and inevitable in almost any cosmological model.

 

[edpell]

the frame in which the average Doppler shift of the CMB vanishes

This frame can be identified. Is there any use we can make of it? Does it do us any good? Is it just an artifact of natural history and "relativity" still being true is of no use? Particularly with respect to the question of inertia and linear frame dragging?