Re: Is this serious?

Bill Hobba wrote:
However, it is well known, Einstein's original formulation of GR had issues, eg Kretchmann pointed out - and Einstein eventually agreed - that the principle of general covariance had no physical content.

Yes.


Bottom line is that our knowledge of GR has moved on since Einstein's time,

Yes. Enormously!


and regardless, of if he thought gravity was space-time curvature, or not, that is now not the general consensus.

Hmmm. I think the consensus is more subtle: the notion of "what gravity is" is not particularly well defined. That is, any single definition of "what gravity is" has numerous counterexamples. While indeed any non-flat manifold is considered to have "gravity", there are some flat manifolds that do so too:

A) the "domain wall" metric is flat everywhere except on the
infinitesimally thick wall itself [@], yet test particles are
attracted to the wall in what one could only describe as a
"uniform gravitational field" (in a region with Riemann=0).

B) a flat manifold with topology SxR^3, in which timelike geodesics
can be spatially closed -- in this case one can select
coordinates that almost cover the manifold [#] in which the
Christoffel symbols are identically zero; geodesics do not
converge, and yet there is some sort of "gravity" present to
permit timelike geodesics to close on themselves.

There are others....

[@] where Riemann is not well defined, so what "curvature"
means is also not well defined.

[#] i.e. they cover it except for a set of measure zero.


As I keep repeating in various contexts: rather than worrying about "what gravity is" (or trying to "measure" it), one should rather be concerned with testing theories.


Tom Roberts
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