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The importance of this account of history is that it gives some perspective in the modification of general relativity that results in an $S^4(1/h)$ background. Technically the modification is to minimize an Einstein-Hilbert action not over all metrics on a fixed three-dimensional manifold but over all hypersurfaces $M$ of $S^4(1/h)$. In order to be completely consistent with classical general relativity, one considers Lorentzian metrics on $S^4(1/h)\times\mathbf{R}$ but the issues are clearer in the space-only analysis. For any hypersurface $M$ of $S^4(1/h)$ and any point $x\in M$ there is a unique normal geodesic which is a circle of length $1/\bar{h}$. Here we can see the room to fit electromagnetism in terms of scale but interestingly we are not dealing with the total space of a circle-bundle. In other words electromagnetism may be fitted geometrically here with gravity (which involves choice of a hypersurface) but the resulting electromagnetic theory will not necessarily be invariant under a circle-action because there is not always a away to deform $M$ along these circles without changing the metric on $M$.
Now Kaluza-Klein theories have been considering products with $M\times S^1$ with a circle of microscopic radius for a long period. Based on the strong bias towards three macroscopic space dimensions on apparently empirical grounds one would reject an $S^4(1/h)$ universe but in the latter case the homogeneity of the the directions can allow an interpretation of the experienced three macroscopic spatial dimensions in terms of four fundamental spatial dimensions.