Dense space / curved space time equivalence
In all scenarios curved space
and dense space are mathematically and geometrically equivalent.
In the example of light being
curved around the sun, if we consider the light traveling in a channel of space
with height equal to the amplitude of the light, the bottom of the channel
appears to have denser space (the wave troughs are closer together) that the top
of the channel, and is an exact equivalent of a band of varying density space.
If we consider the light to be traveling in a region comprised of an infinite
number of number of infinitely thin curved space lines, this is also
mathematically and observationally equivalent to a region with a varying
density of space.
So:
1 - They are the same
thing, and they are equally valid.
2 - No experiment can be
made to distinguish one from the other
Dr Siepmann comments that variable density space is a
refinement of our understanding of space time and that it brings us a little
closer to the truth. He also correctly points out that thinking of space density
implies something with a physical existence, rather than space time which refers
to a quality of the environment, allowing the term to be employed more widely.