There is some discussion about the expansion "of space" in a thread that actually belongs to a different topic so I thought I'd start a thread about that with my input here. Consider the Robertson Walker metric in the following form

[tex]ds^2 = dct^2 - \frac{R^2}{R_{0}^2}\frac{d\rho ^2 + \rho^2 (d\theta ^2 + sin^{2}\theta d\phi ^2)}{(1 + \frac{1}{4}k(\frac{\rho}{R_{0}})^2)^2}[/tex]

Where R is a function of t. This metric represents the expanding universe and specifically what is expanding is the R term. If k = + 1 then the universe is positively closed curved and spacelike hypersurfaces can be taken from this spacetime that are conceivable as balloon like spheres embedded within a hyperspace where R would be the radius of the surface and would then have the interpretation of being the radius of the universe. So, when one talks of the radius of the universe or of the universe as expanding then it is this term changing in time that is being referred to. Some people more convinced that the universe is open curved don't like to think of the universe as having a radius and so call R by scale factor or whatever, but even then R still has the interpretation of the "radius of curvature" of the universe. It is still this radius of curvature that is actually expanding. Now the positions of comoving galaxies are constant with respect to the choice of coordinates expressed in this metric. Their coordinate velocities are zero. The fact that we observe them to be separating is because we are using a rigid ruler extension so to speed of local Cartesian coordinates to describe them instead of the choice of coordinates expressed in this metric. In a sufficiently local limit their rigid ruler velocities are related to the Doppler shift we see by the same formula that gives special relativistic Doppler shifts. So, in a sufficiently local limit saying the galaxies are stationary with respect to a coordinate frame according to which space itself is expanding is equivalent to saying that the galaxies are moving with respect to another coordinate frame according to which space is static. However when one considers the global behavior of the metric and the galaxies one can no longer use the special relativistic Doppler formula, nor the special relativistic metric. One instead finds that the metric in a global description is dynamic according to every frame and so globally speaking it is expanding space and not galaxies separating within space that is the accurate description.

[tex]ds^2 = dct^2 - \frac{R^2}{R_{0}^2}\frac{d\rho ^2 + \rho^2 (d\theta ^2 + sin^{2}\theta d\phi ^2)}{(1 + \frac{1}{4}k(\frac{\rho}{R_{0}})^2)^2}[/tex]

Where R is a function of t. This metric represents the expanding universe and specifically what is expanding is the R term. If k = + 1 then the universe is positively closed curved and spacelike hypersurfaces can be taken from this spacetime that are conceivable as balloon like spheres embedded within a hyperspace where R would be the radius of the surface and would then have the interpretation of being the radius of the universe. So, when one talks of the radius of the universe or of the universe as expanding then it is this term changing in time that is being referred to. Some people more convinced that the universe is open curved don't like to think of the universe as having a radius and so call R by scale factor or whatever, but even then R still has the interpretation of the "radius of curvature" of the universe. It is still this radius of curvature that is actually expanding. Now the positions of comoving galaxies are constant with respect to the choice of coordinates expressed in this metric. Their coordinate velocities are zero. The fact that we observe them to be separating is because we are using a rigid ruler extension so to speed of local Cartesian coordinates to describe them instead of the choice of coordinates expressed in this metric. In a sufficiently local limit their rigid ruler velocities are related to the Doppler shift we see by the same formula that gives special relativistic Doppler shifts. So, in a sufficiently local limit saying the galaxies are stationary with respect to a coordinate frame according to which space itself is expanding is equivalent to saying that the galaxies are moving with respect to another coordinate frame according to which space is static. However when one considers the global behavior of the metric and the galaxies one can no longer use the special relativistic Doppler formula, nor the special relativistic metric. One instead finds that the metric in a global description is dynamic according to every frame and so globally speaking it is expanding space and not galaxies separating within space that is the accurate description.

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