Tom Roberts,

For some reason I was unable to post a reply in the original thread,
so I am starting a new one.

Heimdall

I was contemplating how to visualize the universe expanding when it
struck me that instead of thinking of the universe as expanding,
you could think of matter as shrinking.

That works for a scale-independent theory like Newtonian mechanics,
classical electrodynamics, or GR. But we know that we live in a
quantum
world, and quantum phenomena have an inherent scale. So you cannot do
this and remain consistent with what we already know and observe
about
the world.

What do you mean by "quantum phenomena have an inherent scale"? Can
you give me a simple example and explain why it is not consistent with
the notion of objects shrinking as they enter a more intense
gravitational field?

If not, do you have a link or a book you could reference?

....

What Cartan did is not what you claim above.

I have seen conflicting-sounding claims about what Cartan did. One
was that he proposed a theory that has not yet been experimentally
invalidated. The other was that he did as I said. Another was that
he proposed a family of theories, one of which is equivalent to GR.

It is difficult to see how Cartan could have a theory based on
Euclidean space that gives results not experimentally (maybe I should
add "or observationally") so far distinguishable from GR that doesn't
involve "shrinkage".

I also found a referee's comment, made in rejecting a paper by
somebody named Schmelzer (I think), stating that Schmelzer's
formulation of a GR equivalent theory in Euclidean space was not of
interest because everybody knew you could do that already.

What is your opinion of what Cartan did? How confident are you of
your opinion and why?

But there is a theoretical model that is locally equivalent to GR
that
postulates gravitational interactions on a flat spacetime. See, e.g.
Weinberg. It's much more recent than Cartan, AFAIK.

Here also can you include a reference?